Groupe d’études et de recherche en analyse des décisions

Distribution-Free Optimization for Decision-Making Problems Under Uncertainty: Applications to Option Pricing

Luis Zuluaga Lehigh University, États-Unis

The presence of uncertainty is inherent in key parameters driving decision-making processes. As a result, decision-making problems where it is crucial to acknowledge the uncertainty of the problem parameters arise in a very wide range of areas, such as healthcare, actuarial science, combinatorial optimization, electrical engineering, finance, simulation, physics, revenue management, and supply-chain management. Currently, there are two mainstream solution approaches for this type of decision-making problems under uncertainty: Stochastic Programming (SP), and Robust Optimization (RO). In this talk, we will talk about Distribution-free optimization, an approach that lies in "the midst" of SP and RO. By Distribution-free optimization, we refer to optimization techniques where only partial knowledge of the uncertain parameters' distribution is used to characterize the best solution of the associated decision-making problem. We will begin the talk by introducing some classical examples of applications of Distribution free optimization in probability, inventory, and option pricing. Then, we will focus on presenting recent extensions of these results in the context of risk-averse inventory policies, and specially in the context of pricing basket options; that is, options whose payoff depends on the value of a basket of underlying assets. The use of distribution-free techniques in this context is useful when the structure of the option is too complex to develop analytical or simulation valuation methods, or when the high volatility or scarcity of the data makes it difficult to make strong distributional assumptions on the underlying risk factors. Even when distributional assumptions can be made, and analytical valuation formulas can be developed, distribution-free techniques are useful to check the consistency of such assumptions. We will finish by discussing some directions of future work.