Related papers: Portfolio Optimization under Shortfall Risk Constr…
Motivated by the asset-liability management of a nuclear power plant operator, we consider the problem of finding the least expensive portfolio, which outperforms a given set of stochastic benchmarks. For a specified loss function, the…
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…
This paper studies duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in 1976. We derive an explicit dual problem in terms of two dual variables, one of which is the…
The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular,…
This paper analyzes a problem of optimal static hedging using derivatives in incomplete markets. The investor is assumed to have a risk exposure to two underlying assets. The hedging instruments are vanilla options written on a single…
We consider the classical optimal dividends problem under the Cram\'er-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness…
We consider the problem of estimating and optimizing utility-based shortfall risk (UBSR) of a loss, say $(Y - \hat Y)^2$, in the context of a regression problem. Empirical risk minimization with a UBSR objective is challenging since UBSR is…
The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in…
Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of…
We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in a previous paper under…
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
This paper studies finite-time optimal consumption-investment problems with power, logarithmic and exponential utilities, in a regime switching market with random coefficients, subject to coupled constraints on the consumption and…
We consider the optimization of active extension portfolios. For this purpose, the optimization problem is rewritten as a stochastic programming model and solved using a clever multi-start local search heuristic, which turns out to provide…
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…
Social utility maximization refers to the process of allocating resources in such a way that the sum of agents' utilities is maximized under the system constraints. Such allocation arises in several problems in the general area of…
We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk free asset and in a risky asset, governed by the Black-Scholes equation. There is a…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
Hydro storage system optimization is becoming one of the most challenging tasks in Energy Finance. While currently the state-of-the-art of the commercial software in the industry implements mainly linear models, we would like to introduce…
We consider the problem of optimizing a portfolio of financial assets, where the number of assets can be much larger than the number of observations. The optimal portfolio weights require estimating the inverse covariance matrix of excess…