In this paper we discuss representations of law invariant coherent risk measures in a form of integrals of the Average Value-at-Risk measures. We show that such integral representation exists iff the dual set of the considered risk measure is generated by one of its elements, and this representation is uniquely defined. On the other hand, … Read more
We consider the problem of optimal decision making under uncertainty but assume that the decision maker’s utility function is not completely known. Instead, we consider all the utilities that meet some criteria, such as preferring certain lotteries over certain other lotteries and being risk averse, s-shaped, or prudent. This extends the notion of stochastic dominance. … Read more
This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous … Read more
This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous … Read more
We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is forced to be below a low-risk threshold with a large probability, thereby limiting … Read more
We present a new approach for portfolio selection when the underlying distribution of asset returns is uncertain or ambiguous to investors. In particular, we consider the case that an investor can formulate some reference financial models based on his/her prior beliefs or information, but is concerned about misspecification of the reference models and the associated … Read more
In recent years the robust counterpart approach, introduced and made popular by Ben-Tal, Nemirovski and El Ghaoui, gained more and more interest among both academics and practitioners. However, to the best of our knowledge, only very few results on the relationship between the original problem instance and the robust counterpart have been established. This exposition … Read more
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a … Read more
We consider the problem of dynamic portfolio optimization in a discrete-time, finite-horizon setting. Our general model considers risk aversion, portfolio constraints (e.g., no short positions), return predictability, and transaction costs. This problem is naturally formulated as a stochastic dynamic program. Unfortunately, with non-zero transaction costs, the dimension of the state space is at least as … Read more
A.D.Roy’s (1952) safety first (SF) approach to a financial portfolio selection is improved. Safety first means minimization of probability of poor returns. Improvement concerns a better estimation of the poor return probabilities by means of shortfall risk functions. Optimal SF-portfolio is sought similar to Roy’s geometric method but with a different efficient frontier. In case … Read more