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The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge…
We consider a class of generalized capital asset pricing models in continuous time with a finite number of agents and tradable securities. The securities may not be sufficient to span all sources of uncertainty. If the agents have…
We present a new discrete time version of Kyle's (1985) classic model of insider trading, formulated as a generalised extensive form game. The model has three kinds of traders: an insider, random noise traders, and a market maker. The…
In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy.…
This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The…
This paper studies the optimal consumption under the addictive habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multi-asset…
We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization…
A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness.…
We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing…
Bilateral trade is a fundamental economic scenario comprising a strategically acting buyer and seller, each holding valuations for the item, drawn from publicly known distributions. A mechanism is supposed to facilitate trade between these…
We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval…
We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that…
We introduce a system of kinetic equations describing an exchange market consisting of two populations of agents (dealers and speculators) expressing the same preferences for two goods, but applying different strategies in their exchanges.…
We develop a game-theoretic framework for the study of competition between firms who have budgets to "seed" the initial adoption of their products by consumers located in a social network. The payoffs to the firms are the eventual number of…
Efficient markets are characterised by profit-driven participants continuously refining their positions towards the latest insights. Margins for profit generation are generally small, shaping a difficult landscape for automated trading…
We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol…
Consider a trade market with one seller and multiple buyers. The seller aims to sell an indivisible item and maximize their revenue. This paper focuses on a simple and popular mechanism--the fixed-price mechanism. Unlike the standard…
We consider continuous-time mean-field stochastic games with strategic complementarities. The interaction between the representative productive firm and the population of rivals comes through the price at which the produced good is sold and…
In a continuous time stochastic economy, this paper considers the problem of consumption and investment in a financial market in which the representative investor exhibits a change in the discount rate. The investment opportunities are a…
We consider a class of learning problems in which an agent liquidates a risky asset while creating both transient price impact driven by an unknown convolution propagator and linear temporary price impact with an unknown parameter. We…