List of presentations and abstracts
Title: Utility Maximization without Reasonable Asymptotic Elasticity
Abstract: For utility functions U finite only on the positive real line, Kramkov and Schachermayer showed that under a condition on U, the well- known Reasonable Asymptotic Elasticity, the associated utility maximization problem has a (unique) optimal solution, independently of the probabilistic model.What about the relaxed investor, whose utility does not satisfy RAE? This has been also addressed by Kramkov and Schachermayer, but the optimal solution is characterized only for sufficiently small initial endowments. Under a sufficient (and basically necessary) joint condition on the probabilistic model and the utility, we show by relaxation and duality techniques that the maximization problem admits solution for any initial endowment. However, a singular part may pop up, that is the optimal investment may have a component which is concentrated on a set of probability zero. This singular part may fail to be unique. This is joint work with P. Guasoni
Title: A duality theory for set--valued risk measures and applications
Abstract: Jouini et al. (Finance & Stochastics 8, 2004) proposed the concept of set–valued coherent
risk measures in order to incorporate market frictions like exchange rates, transaction costs
or liquidity bounds in the evaluation of the risk of a portfolio consisting of d ! 1 assets.
The basic question is how to quantify the risk of a vector position (with d components)
in terms of a cash vector (with m components where d " m in most cases).
Alexander Schied (Cornell University)
Title: Convex and nonlinear optimization problems for large traders
Abstract: We consider the problem of finding optimal liquidation strategies for a large portfolio in an illiquid market. Standard optimality criteria are the minimization of the expected liquidity costs or the maximization of the expected utility of the revenues. Depending on the model used to describe an illiquid market, this leads to a convex optimization problem or to even more general nonlinearities. The talk will in particular highlight the convexity aspects of this problem.
Mihai Sirbu (UT Austin)
Title:In which Financial Markets do Mutual Fund Theorems hold true?
Abstract: The Mutual Fund Theorem (MFT) is considered in a general semimartingale
financial market S with a finite time horizon T, where agents
maximize expected utility of terminal wealth. The main results are:
2: If for a given class of utility functions (i.e. investors) the (MFT) holds true in all complete Brownian financial markets $S$, then all investors use the same utility function U, which must be of HARA type. This is a result in the spirit of the classical work by Cass and Stiglitz.
This is joint work with Walter Schachermayer and Erik Taflin.
Mike Tehranchi (Cambridge University)
Title: Forward utility and consumption
Abstract: Recently, the notion of time-consistent utility functions has appeared in the mathematical finance literature. In our framework, a forward utility is a family of adapted $(t,\omega)$-dependent utility functions which satisfy the dynamic programming principle for a Merton investment problem. Working in a fairly general (possibly incomplete) market, we present a dual characterization of the pure investment and mixed investment/consumption forward utility functions.
Mingxin Xu (UNC-Charlotte)
Title: Risk Minimizing Portfolio Optimization and Hedging with Conditional Value-at-Risk
Abstract: We look at the problem of how to find a dynamic optimal portfolio so that the Conditional Value-at-Risk (CVaR) is minimized under the condition where the returns are bounded. CVaR is a coherent risk measure based on the popular VaR. In a complete market setting, we derive the exact optimal conditions. Then we provide applications in two classic complete market models: the Binomial model and the Black-Scholes model. In these cases, the procedures to find the optimal strategies are given with exact formulas. Numerical results show, as expected, dynamic portfolio provide much lower CVaR risk than static portfolios.
Thaleia Zariphopoulou (University of Texas Austin)
Title: Bespoke portfolios and implied preferences
Abstract: In my talk I will discuss how the preferences of an investor can be inferred by his/her investment "wish-list". The analysis uses arguments from the forward utility approach and is applicable to a variety of models. Examples for the case of deterministic market price of risk will be presented.
Statistics & Applied Probability
University of California
Santa Barbara, California 93106-3110