Browsing by Subject "Coherent risk measures"

Now showing 1 - 4 of 4

Open Access
Measures of model uncertainty and calibrated option bounds
(Taylor & Francis, 2009) Pınar, M. Ç.
Recently, Cont introduced a quantitative framework for measuring model uncertainty in the context of derivative pricing [Model uncertainty and its impact on the pricing of derivative instruments, Math. Finance, 16(3) (2006), pp. 519-547]. Two measures of model uncertainty were proposed: one measure based on a coherent risk measure compatible with market prices of derivatives and another measure based on convex risk measures. We show in a discrete time, finite state probability setting, that the two measures introduced by Cont are closely related to calibrated option bounds studied recently by King et al. [Calibrated option bounds, Inf. J. Ther. Appl. Financ., 8(2) (2005), pp. 141-159]. The precise relationship is established through convex programming duality. As a result, the model uncertainty measures can be computed efficiently by solving convex programming or linear programming problems after a suitable discretization. Numerical results using S&P 500 options are given.
Open Access
Optimal timing of living-donor liver transplantation under risk-aversion
(2016-07) Köse, Ümit Emre
Liver transplantation, which can be performed from either living-donors or cadavers, is the only viable treatment for end-stage liver diseases. In this study, we focus on living-donor liver transplantation. The timing of the transplantation from a living-donor is crucial as it affects the quality and the length of the patient's lifetime. The studies in the literature use risk-neutral Markov decision processes (MDPs) to optimize the timing of transplantation. However, in real life, the patients and the physicians are usually risk-averse, therefore, those risk neutral models fail to represent the real behavior. In this study, we model the living-donor liver transplantation problem as a risk-averse MDP. We incorporate risk-aversion into the MDP model using dynamic coherent measures of risk, and in order to be able to re ect varying risk preferences of the decision makers, we use first-order mean-semi-deviation and mean-AVaR as the one-step conditional measures of risk. We obtain optimal policies for patients having cirrhotic diseases or hepatitis B under different risk preferences and organs of different quality. We also measure the sensitivity of the optimal policies to the transition probabilities and to the quality of life. We further perform a simulation study in order to find the distribution of lifetime under the risk-averse optimal policies.
Open Access
Risk-averse allocation indices for multiarmed bandit problem
(IEEE, 2021-01-25) Malekipirbazari, Milad; Çavuş, Özlem
In classical multiarmed bandit problem, the aim is to find a policy maximizing the expected total reward, implicitly assuming that the decision-maker is risk-neutral. On the other hand, the decision-makers are risk-averse in some real-life applications. In this article, we design a new setting based on the concept of dynamic risk measures where the aim is to find a policy with the best risk-adjusted total discounted outcome. We provide a theoretical analysis of multiarmed bandit problem with respect to this novel setting and propose a priority-index heuristic which gives risk-averse allocation indices having a structure similar to Gittins index. Although an optimal policy is shown not always to have index-based form, empirical results express the excellence of this heuristic and show that with risk-averse allocation indices we can achieve optimal or near-optimal interpretable policies.
Open Access
Risk-averse multi-armed bandit problem
(2021-08) Malekipirbazari, Milad
In classical multi-armed bandit problem, the aim is to ﬁnd a policy maximizing the expected total reward, implicitly assuming that the decision maker is risk-neutral. On the other hand, the decision makers are risk-averse in some real life applications. In this study, we design a new setting for the classical multi-armed bandit problem (MAB) based on the concept of dynamic risk measures, where the aim is to ﬁnd a policy with the best risk adjusted total discounted outcome. We provide theoretical analysis of MAB with respect to this novel setting, and propose two diﬀerent priority-index heuristics giving risk-averse allocation indices with structures similar to Gittins index. The ﬁrst proposed heuristic is based on Lagrangian duality and the indices are expressed as the Lagrangian multiplier corresponding to the activation constraint. In the second part, we present a theoretical analysis based on Whittle’s retirement problem and propose a gener-alized version of restart-in-state formulation of the Gittins index to compute the proposed risk-averse allocation indices. Finally, as a practical application of the proposed methods, we focus on optimal design of clinical trials and we apply our risk-averse MAB approach to perform risk-averse treatment allocation based on a Bayesian Bernoulli model. We evaluate the performance of our approach against other allocation rules, including ﬁxed randomization.