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We provide a new algorithm for solving Risk Sensitive Partially Observable Markov Decisions Processes, when the risk is modeled by a utility function, and both the state space and the space of observations is finite. This algorithm is based…
In an equity market model with "Knightian" uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative…
We prove existence and uniqueness of stochastic equilibria in a class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and…
Equity premium, the surplus returns of stocks over bonds, has been an enduring puzzle. While numerous prior works approach the problem assuming the utility of money is invariant across contexts, our approach implies that in efficient…
We study the ex-ante minimization of market inefficiency, defined in terms of minimum deviation of market prices from fundamental values, from a centralized planner's perspective. Prices are pressured from exogenous trading actions of…
We study a portfolio management problem featuring many-player and mean field competition, investment and consumption, and relative performance concerns under the forward performance processes (FPP) framework. We focus on agents using power…
We consider the problem of an agent who faces losses in continuous time over a finite time horizon and may choose to share some of these losses with a counterparty. The agent is uncertain about the true loss distribution and has multiple…
We consider the forward investment problem in market models where the stock prices are continuous semimartingales adapted to a Brownian filtration. We construct a broad class of forward performance processes with initial conditions of power…
The paper [12] examines a concept of equilibrium policies instead of optimal controls in stochastic optimization to analyze a mean-variance portfolio selection problem. We follow the same approach in order to investigate the Merton…
We present an approach for pricing European call options in presence of proportional transaction costs, when the stock price follows a general exponential L\'{e}vy process. The model is a generalization of the celebrated work of Davis,…
This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by It\^o-L\'evy processes, but it also contains some new results on the underlying stochastic maximum…
We study superreplication of European contingent claims in discrete time in a large trader model with market indifference prices recently proposed by Bank and Kramkov. We introduce a suitable notion of efficient friction in this framework,…
In this work we present an equilibrium formulation for price impacts. This is motivated by the Buhlmann equilibrium in which assets are sold into a system of market participants, e.g. a fire sale in systemic risk, and can be viewed as a…
We first study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high-dimensional setting where p, the number of variables in the problem, is of the same order…
We consider models of financial markets in which all parties involved find incentives to participate. Strategies are evaluated directly by their virtual wealths. By tuning the price sensitivity and market impact, a phase diagram with…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
A Markovian modulation captures the trend in the market and influences the market coefficients accordingly. The different scenarios presented by the market are modeled as the distinct states of a discrete-time Markov chain. In our paper, we…
We consider the problem of optimal investment and consumption in a class of multidimensional jump-diffusion models in which asset prices are subject to mutually exciting jump processes. This captures a type of contagion where each downward…
We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…