Related papers: Robust no arbitrage and the solvability of vector-…
Experimental results on market behavior establish a lower stability and efficiency of markets for durable re-tradable assets compared to markets for non-durable, or perishable, goods. In this chapter, we revisit this known but…
We solve a min-max problem in a robust exploratory mean-variance problem with drift uncertainty in this paper. It is verified that robust investors choose the Sharpe ratio with minimal $L^2$ norm in an admissible set. A reinforcement…
We consider the scenario where $N$ utilities strategically bid for electricity in the day-ahead market and balance the mismatch between the committed supply and actual demand in the real-time market, with uncertainty in demand and local…
We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex…
Stability of the utility maximization problem with random endowment and indifference prices is studied for a sequence of financial markets in an incomplete Brownian setting. Our novelty lies in the nonequivalence of markets, in which the…
We prove that the problem of computing an Arrow-Debreu market equilibrium is PPAD-complete even when all traders use additively separable, piecewise-linear and concave utility functions. In fact, our proof shows that this market-equilibrium…
We consider a nonlinear pricing environment with private information. We provide profit guarantees (and associated mechanisms) that the seller can achieve across all possible distributions of willingness to pay of the buyers. With a…
The strong relative arbitrage problem in Stochastic Portfolio Theory seeks an investment strategy that almost surely outperforms a benchmark portfolio at the end of a given time horizon. The highest relative return in relative arbitrage…
We derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Ito process or a positive diffusion with Markov switching. In particular,…
We solve in closed-form an equilibrium model in which a finite number of exponential investors continuously consume and trade with price-impact. Compared to the analogous Pareto-efficient equilibrium model, price-impact has an amplification…
We study a problem of utility maximization under model uncertainty with information including jumps. We prove first that the value process of the robust stochastic control problem is described by the solution of a quadratic-exponential…
We analyze the efficiency of markets with friction, particularly power markets. We model the market as a dynamic system with $(d_t;\,t\geq 0)$ the demand process and $(s_t;\,t\geq 0)$ the supply process. Using stochastic differential…
We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bid-ask spread and temporary market price impact penalizing speedy execution trades. We use a continuous-time modeling framework, but in…
This paper investigates a Pareto optimal insurance problem, where the insured maximizes her rank-dependent utility preference and the insurer is risk neutral and employs the mean-variance premium principle. To eliminate potential moral…
This paper studies convex duality in optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions…
We consider a stochastic financial incomplete market where the price processes are described by a vector-valued semimartingale that is possibly nonlocally bounded. We face the classical problem of utility maximization from terminal wealth,…
We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification and in preferences and…
We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic…
In a discrete time setting, we study the central problem of giving a fair price to some financial product. For several decades, the no-arbitrage conditions and the martingale measures have played a major role for solving this problem. We…
We derive tractable necessary and sufficient conditions for the absence of buy-and-hold arbitrage opportunities in a perfectly liquid, one period market. We formulate the positivity of Arrow-Debreu prices as a generalized moment problem to…