Добірка наукової літератури з теми "Singular jump-diffusion process"

AbstractWe study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.

This paper proposes an equilibrium model for evaluating equity with optimal dividend policy in a jump-diffusion market. In this model, a representative investor having power utility over an aggregate consumption process evaluates the equity as the expected value of the discounted dividends with his stochastic discount factor, while a firm paying the dividends from its own cash reserves manages to maximize the equity price. This situation is formulated as a singular stochastic control problem of jump-diffusion processes. We solve this problem and give the equilibrium equity price and the optimal dividend policy. Numerical examples show that the aggregate consumption process and the investor’s risk aversion have a significant impact on the equity price and the dividend policy. This model provides a structural explanation of equity risk premiums that is consistent with the standard theory of asset pricing.

AbstractWe study a financial market where the risky asset is modelled by a geometric Itô-Lévy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier. See e.g. Jarrow and Protter (J Bank Finan 29:2803–2820, 2005) for an explanation and discussion of this model in the Brownian motion case. As already pointed out by Karatzas and Shreve (Methods of Mathematical Finance, Springer, Berlin, 1998) (in the continuous setting), this allows for arbitrages in the market. However, the situation in the case of jumps is not clear. Moreover, it is not clear what happens if there is a delay in the system. In this paper we consider a jump diffusion market model with a singular drift term modelled as the local time of a given process, and with a delay $$\theta > 0$$ θ > 0 in the information flow available for the trader. We allow the stock price dynamics to depend on both a continuous process (Brownian motion) and a jump process (Poisson random measure). We believe that jumps and delays are essential in order to get more realistic financial market models. Using white noise calculus we compute explicitly the optimal consumption rate and portfolio in this case and we show that the maximal value is finite as long as $$\theta > 0$$ θ > 0 . This implies that there is no arbitrage in the market in that case. However, when $$\theta $$ θ goes to 0, the value goes to infinity. This is in agreement with the above result that is an arbitrage when there is no delay. Our model is also relevant for high frequency trading issues. This is because high frequency trading often leads to intensive trading taking place on close to infinitesimal lengths of time, which in the limit corresponds to trading on time sets of measure 0. This may in turn lead to a singular drift in the pricing dynamics. See e.g. Lachapelle et al. (Math Finan Econom 10(3):223–262, 2016) and the references therein.

Introduction Explorations of the multimedia game format within cultural studies have been broadly approached from two perspectives: one -- the impact of technologies on user interaction particularly with regard to social implications, and the other -- human computer interactions within the framework of cybercultures. Another approach to understanding or speaking about games within cultural studies is to focus on the game experience as cultural practice -- as an activity or an event. In this article I wish to initiate an exploration of the aesthetics of player space as a distinctive element of the gameplay experience. In doing so I propose that an understanding of aesthetic spatial issues as an element of player interactivity and engagement is important for understanding the cultural practice of adventure gameplay. In approaching these questions, I am focussing on the single-player exploration adventure game in particular Myst and The Crystal Key. In describing these games as adventures I am drawing on Chris Crawford's The Art of Computer Game Design, which although a little dated, focusses on game design as a distinct activity. He brings together a theoretical approach with extensive experience as a game designer himself (Excalibur, Legionnaire, Gossip). Whilst at Atari he also worked with Brenda Laurel, a key theorist in the area of computer design and dramatic structure. Adventure games such as Myst and The Crystal Key might form a sub-genre in Chris Crawford's taxonomy of computer game design. Although they use the main conventions of the adventure game -- essentially a puzzle to be solved with characters within a story context -- the main focus and source of pleasure for the player is exploration, particularly the exploration of worlds or cosmologies. The main gameplay of both games is to travel through worlds solving clues, picking up objects, and interacting with other characters. In Myst the player has to solve the riddle of the world they have entered -- as the CD-ROM insert states "Now you're here, wherever here is, with no option but to explore." The goal, as the player must work out, is to release the father Atrus from prison by bringing magic pages of a book to different locations in the worlds. Hints are offered by broken-up, disrupted video clips shown throughout the game. In The Crystal Key, the player as test pilot has to save a civilisation by finding clues, picking up objects, mending ships and defeating an opponent. The questions foregrounded by a focus on the aesthetics of navigation are: What types of representational context are being set up? What choices have designers made about representational context? How are the players positioned within these spaces? What are the implications for the player's sense of orientation and navigation? Architectural Fabrication For the ancient Greeks, painting was divided into two categories: magalography (the painting of great things) and rhyparography (the painting of small things). Magalography covered mythological and historical scenes, which emphasised architectural settings, the human figure and grand landscapes. Rhyparography referred to still lifes and objects. In adventure games, particularly those that attempt to construct a cosmology such as Myst and The Crystal Key, magalography and rhyparography collide in a mix of architectural monumentality and obsessive detailing of objects. For the ancient Greeks, painting was divided into two categories: magalography (the painting of great things) and rhyparography (the painting of small things). Magalography covered mythological and historical scenes, which emphasised architectural settings, the human figure and grand landscapes. Rhyparography referred to still lifes and objects. In adventure games, particularly those that attempt to construct a cosmology such as Myst and The Crystal Key, magalography and rhyparography collide in a mix of architectural monumentality and obsessive detailing of objects. The creation of a digital architecture in adventure games mimics the Pompeii wall paintings with their interplay of extruded and painted features. In visualising the space of a cosmology, the environment starts to be coded like the urban or built environment with underlying geometry and textured surface or dressing. In The Making of Myst (packaged with the CD-ROM) Chuck Carter, the artist on Myst, outlines the process of creating Myst Island through painting the terrain in grey scale then extruding the features and adding textural render -- a methodology that lends itself to a hybrid of architectural and painted geometry. Examples of external architecture and of internal room design can be viewed online. In the spatial organisation of the murals of Pompeii and later Rome, orthogonals converged towards several vertical axes showing multiple points of view simultaneously. During the high Renaissance, notions of perspective developed into a more formal system known as the construzione legittima or legitimate construction. This assumed a singular position of the on-looker standing in the same place as that occupied by the artist when the painting was constructed. In Myst there is an exaggeration of the underlying structuring technique of the construzione legittima with its emphasis on geometry and mathematics. The player looks down at a slight angle onto the screen from a fixed vantage point and is signified as being within the cosmological expanse, either in off-screen space or as the cursor. Within the cosmology, the island as built environment appears as though viewed through an enlarging lens, creating the precision and coldness of a Piero della Francesca painting. Myst mixes flat and three-dimensional forms of imagery on the same screen -- the flat, sketchy portrayal of the trees of Myst Island exists side-by-side with the monumental architectural buildings and landscape design structures created in Macromodel. This image shows the flat, almost expressionistic trees of Myst Island juxtaposed with a fountain rendered in high detail. This recalls the work of Giotto in the Arena chapel. In Joachim's Dream, objects and buildings have depth, but trees, plants and sky -- the space in-between objects -- is flat. Myst Island conjures up the realm of a magic, realist space with obsolete artefacts, classic architectural styles (the Albert Hall as the domed launch pad, the British Museum as the library, the vernacular cottage in the wood), mechanical wonders, miniature ships, fountains, wells, macabre torture instruments, ziggurat-like towers, symbols and odd numerological codes. Adam Mates describes it as "that beautiful piece of brain-deadening sticky-sweet eye-candy" but more than mere eye-candy or graphic verisimilitude, it is the mix of cultural ingredients and signs that makes Myst an intriguing place to play. The buildings in The Crystal Key, an exploratory adventure game in a similar genre to Myst, celebrate the machine aesthetic and modernism with Buckminster Fuller style geodesic structures, the bombe shape, exposed ducting, glass and steel, interiors with movable room partitions and abstract expressionist decorations. An image of one of these modernist structures is available online. The Crystal Key uses QuickTime VR panoramas to construct the exterior and interior spaces. Different from the sharp detail of Myst's structures, the focus changes from sharp in wide shot to soft focus in close up, with hot-spot objects rendered in trompe l'oeil detail. The Tactility of Objects "The aim of trompe l'oeil -- using the term in its widest sense and applying it to both painting and objects -- is primarily to puzzle and to mystify" (Battersby 19). In the 15th century, Brunelleschi invented a screen with central apparatus in order to obtain exact perspective -- the monocular vision of the camera obscura. During the 17th century, there was a renewed interest in optics by the Dutch artists of the Rembrandt school (inspired by instruments developed for Dutch seafaring ventures), in particular Vermeer, Hoogstraten, de Hooch and Dou. Gerard Dou's painting of a woman chopping onions shows this. These artists were experimenting with interior perspective and trompe l'oeil in order to depict the minutia of the middle-class, domestic interior. Within these luminous interiors, with their receding tiles and domestic furniture, is an elevation of the significance of rhyparography. In the Girl Chopping Onions of 1646 by Gerard Dou the small things are emphasised -- the group of onions, candlestick holder, dead fowl, metal pitcher, and bird cage. Trompe l'oeil as an illusionist strategy is taken up in the worlds of Myst, The Crystal Key and others in the adventure game genre. Traditionally, the fascination of trompe l'oeil rests upon the tension between the actual painting and the scam; the physical structures and the faux painted structures call for the viewer to step closer to wave at a fly or test if the glass had actually broken in the frame. Mirian Milman describes trompe l'oeil painting in the following manner: "the repertory of trompe-l'oeil painting is made up of obsessive elements, it represents a reality immobilised by nails, held in the grip of death, corroded by time, glimpsed through half-open doors or curtains, containing messages that are sometimes unreadable, allusions that are often misunderstood, and a disorder of seemingly familiar and yet remote objects" (105). Her description could be a scene from Myst with in its suggestion of theatricality, rich texture and illusionistic play of riddle or puzzle. In the trompe l'oeil painterly device known as cartellino, niches and recesses in the wall are represented with projecting elements and mock bas-relief. This architectural trickery is simulated in the digital imaging of extruded and painting elements to give depth to an interior or an object. Other techniques common to trompe l'oeil -- doors, shadowy depths and staircases, half opened cupboard, and paintings often with drapes and curtains to suggest a layering of planes -- are used throughout Myst as transition points. In the trompe l'oeil paintings, these transition points were often framed with curtains or drapes that appeared to be from the spectator space -- creating a painting of a painting effect. Myst is rich in this suggestion of worlds within worlds through the framing gesture afforded by windows, doors, picture frames, bookcases and fireplaces. Views from a window -- a distant landscape or a domestic view, a common device for trompe l'oeil -- are used in Myst to represent passageways and transitions onto different levels. Vertical space is critical for extending navigation beyond the horizontal through the terraced landscape -- the tower, antechamber, dungeon, cellars and lifts of the fictional world. Screen shots show the use of the curve, light diffusion and terracing to invite the player. In The Crystal Key vertical space is limited to the extent of the QTVR tilt making navigation more of a horizontal experience. Out-Stilling the Still Dutch and Flemish miniatures of the 17th century give the impression of being viewed from above and through a focussing lens. As Mastai notes: "trompe l'oeil, therefore is not merely a certain kind of still life painting, it should in fact 'out-still' the stillest of still lifes" (156). The intricate detailing of objects rendered in higher resolution than the background elements creates a type of hyper-reality that is used in Myst to emphasise the physicality and actuality of objects. This ultimately enlarges the sense of space between objects and codes them as elements of significance within the gameplay. The obsessive, almost fetishistic, detailed displays of material artefacts recall the curiosity cabinets of Fabritius and Hoogstraten. The mechanical world of Myst replicates the Dutch 17th century fascination with the optical devices of the telescope, the convex mirror and the prism, by coding them as key signifiers/icons in the frame. In his peepshow of 1660, Hoogstraten plays with an enigma and optical illusion of a Dutch domestic interior seen as though through the wrong end of a telescope. Using the anamorphic effect, the image only makes sense from one vantage point -- an effect which has a contemporary counterpart in the digital morphing widely used in adventure games. The use of crumbled or folded paper standing out from the plane surface of the canvas was a recurring motif of the Vanitas trompe l'oeil paintings. The highly detailed representation and organisation of objects in the Vanitas pictures contained the narrative or symbology of a religious or moral tale. (As in this example by Hoogstraten.) In the cosmology of Myst and The Crystal Key, paper contains the narrative of the back-story lovingly represented in scrolls, books and curled paper messages. The entry into Myst is through the pages of an open book, and throughout the game, books occupy a privileged position as holders of stories and secrets that are used to unlock the puzzles of the game. Myst can be read as a Dantesque, labyrinthine journey with its rich tapestry of images, its multi-level historical associations and battle of good and evil. Indeed the developers, brothers Robyn and Rand Miller, had a fertile background to draw on, from a childhood spent travelling to Bible churches with their nondenominational preacher father. The Diorama as System Event The diorama (story in the round) or mechanical exhibit invented by Daguerre in the 19th century created a mini-cosmology with player anticipation, action and narrative. It functioned as a mini-theatre (with the spectator forming the fourth wall), offering a peek into mini-episodes from foreign worlds of experience. The Musée Mechanique in San Francisco has dioramas of the Chinese opium den, party on the captain's boat, French execution scenes and ghostly graveyard episodes amongst its many offerings, including a still showing an upper class dancing party called A Message from the Sea. These function in tandem with other forbidden pleasures of the late 19th century -- public displays of the dead, waxwork museums and kinetescope flip cards with their voyeuristic "What the Butler Saw", and "What the Maid Did on Her Day Off" tropes. Myst, along with The 7th Guest, Doom and Tomb Raider show a similar taste for verisimilitude and the macabre. However, the pre-rendered scenes of Myst and The Crystal Key allow for more diorama like elaborate and embellished details compared to the emphasis on speed in the real-time-rendered graphics of the shoot-'em-ups. In the gameplay of adventure games, animated moments function as rewards or responsive system events: allowing the player to navigate through the seemingly solid wall; enabling curtains to be swung back, passageways to appear, doors to open, bookcases to disappear. These short sequences resemble the techniques used in mechanical dioramas where a coin placed in the slot enables a curtain or doorway to open revealing a miniature narrative or tableau -- the closure of the narrative resulting in the doorway shutting or the curtain being pulled over again. These repeating cycles of contemplation-action-closure offer the player one of the rewards of the puzzle solution. The sense of verisimilitude and immersion in these scenes is underscored by the addition of sound effects (doors slamming, lifts creaking, room atmosphere) and music. Geographic Locomotion Static imagery is the standard backdrop of the navigable space of the cosmology game landscape. Myst used a virtual camera around a virtual set to create a sequence of still camera shots for each point of view. The use of the still image lends itself to a sense of the tableauesque -- the moment frozen in time. These tableauesque moments tend towards the clean and anaesthetic, lacking any evidence of the player's visceral presence or of other human habitation. The player's navigation from one tableau screen to the next takes the form of a 'cyber-leap' or visual jump cut. These jumps -- forward, backwards, up, down, west, east -- follow on from the geographic orientation of the early text-based adventure games. In their graphic form, they reveal a new framing angle or point of view on the scene whilst ignoring the rules of classical continuity editing. Games such as The Crystal Key show the player's movement through space (from one QTVR node to another) by employing a disorientating fast zoom, as though from the perspective of a supercharged wheelchair. Rather than reconciling the player to the state of movement, this technique tends to draw attention to the technologies of the programming apparatus. The Crystal Key sets up a meticulous screen language similar to filmic dramatic conventions then breaks its own conventions by allowing the player to jump out of the crashed spaceship through the still intact window. The landscape in adventure games is always partial, cropped and fragmented. The player has to try and map the geographical relationship of the environment in order to understand where they are and how to proceed (or go back). Examples include selecting the number of marker switches on the island to receive Atrus's message and the orientation of Myst's tower in the library map to obtain key clues. A screenshot shows the arrival point in Myst from the dock. In comprehending the landscape, which has no centre, the player has to create a mental map of the environment by sorting significant connecting elements into chunks of spatial elements similar to a Guy Debord Situationist map. Playing the Flaneur The player in Myst can afford to saunter through the landscape, meandering at a more leisurely pace that would be possible in a competitive shoot-'em-up, behaving as a type of flaneur. The image of the flaneur as described by Baudelaire motions towards fin de siècle decadence, the image of the socially marginal, the dispossessed aristocrat wandering the urban landscape ready for adventure and unusual exploits. This develops into the idea of the artist as observer meandering through city spaces and using the power of memory in evoking what is observed for translation into paintings, writing or poetry. In Myst, the player as flaneur, rather than creating paintings or writing, is scanning the landscape for clues, witnessing objects, possible hints and pick-ups. The numbers in the keypad in the antechamber, the notes from Atrus, the handles on the island marker, the tower in the forest and the miniature ship in the fountain all form part of a mnemomic trompe l'oeil. A screenshot shows the path to the library with one of the island markers and the note from Atrus. In the world of Myst, the player has no avatar presence and wanders around a seemingly unpeopled landscape -- strolling as a tourist venturing into the unknown -- creating and storing a mental map of objects and places. In places these become items for collection -- cultural icons with an emphasised materiality. In The Crystal Key iconography they appear at the bottom of the screen pulsing with relevance when active. A screenshot shows a view to a distant forest with the "pick-ups" at the bottom of the screen. This process of accumulation and synthesis suggests a Surrealist version of Joseph Cornell's strolls around Manhattan -- collecting, shifting and organising objects into significance. In his 1982 taxonomy of game design, Chris Crawford argues that without competition these worlds are not really games at all. That was before the existence of the Myst adventure sub-genre where the pleasures of the flaneur are a particular aspect of the gameplay pleasures outside of the rules of win/loose, combat and dominance. By turning the landscape itself into a pathway of significance signs and symbols, Myst, The Crystal Key and other games in the sub-genre offer different types of pleasures from combat or sport -- the pleasures of the stroll -- the player as observer and cultural explorer. References Battersby, M. Trompe L'Oeil: The Eye Deceived. New York: St. Martin's, 1974. Crawford, C. The Art of Computer Game Design. Original publication 1982, book out of print. 15 Oct. 2000 <http://members.nbci.com/kalid/art/art.php>. Darley Andrew. Visual Digital Culture: Surface Play and Spectacle in New Media Genres. London: Routledge, 2000. Lunenfeld, P. Digital Dialectic: New Essays on New Media. Cambridge, Mass.: MIT P 1999. Mates, A. Effective Illusory Worlds: A Comparative Analysis of Interfaces in Contemporary Interactive Fiction. 1998. 15 Oct. 2000 <http://www.wwa.com/~mathes/stuff/writings>. Mastai, M. L. d'Orange. Illusion in Art, Trompe L'Oeil: A History of Pictorial Illusion. New York: Abaris, 1975. Miller, Robyn and Rand. "The Making of Myst." Myst. Cyan and Broderbund, 1993. Milman, M. Trompe-L'Oeil: The Illusion of Reality. New York: Skira Rizzoli, 1982. Murray, J. Hamlet on the Holodeck: The Future of Narrative in Cyberspace. New York: Simon and Schuster, 1997. Wertheim, M. The Pearly Gates of Cyberspace: A History of Cyberspace from Dante to the Internet. Sydney: Doubleday, 1999. Game References 7th Guest. Trilobyte, Inc., distributed by Virgin Games, 1993. Doom. Id Software, 1992. Excalibur. Chris Crawford, 1982. Myst. Cyan and Broderbund, 1993. Tomb Raider. Core Design and Eidos Interactive, 1996. The Crystal Key. Dreamcatcher Interactive, 1999. Citation reference for this article MLA style: Bernadette Flynn. "Towards an Aesthetics of Navigation -- Spatial Organisation in the Cosmology of the Adventure Game." M/C: A Journal of Media and Culture 3.5 (2000). [your date of access] <http://www.api-network.com/mc/0010/navigation.php>. Chicago style: Bernadette Flynn, "Towards an Aesthetics of Navigation -- Spatial Organisation in the Cosmology of the Adventure Game," M/C: A Journal of Media and Culture 3, no. 5 (2000), <http://www.api-network.com/mc/0010/navigation.php> ([your date of access]). APA style: Bernadette Flynn. (2000) Towards an aesthetics of navigation -- spatial organisation in the cosmology of the adventure game. M/C: A Journal of Media and Culture 3(5). <http://www.api-network.com/mc/0010/navigation.php> ([your date of access]).