Browsing by Subject "Risk measures"

Now showing 1 - 3 of 3

Open Access
Decomposable sums and their implications on naturally quasiconvex risk measures
(2020-09) Bilir, Barış
When measuring risk in finance, it is natural to expect that risk decreases with diversification. For risk measures, convexity and quasiconvexity are the two properties which capture the concept of diversification. In between these two properties, there is natural quasiconvexity. Natural quasiconvexity is an old but not so well-known property which is weaker than convexity but stronger than quasiconvexity. In the literature, a lot of effort is put on the analysis of the convexity and the quasiconvexity properties of risk measures. However, a detailed discussion on naturally quasiconvex risk measures is still missing and this thesis aims to fill this gap. Natural quasiconvexity is equivalent to a property called ?-quasiconvexity. By making use of this equivalence, we relate naturally quasiconvex risk measures to additively decomposable sums. A notion called convexity index, which is defined in in the literature in 1980s, plays a crucial role in the discussion of additively decomposable sums. Next, we turn our attention to naturally quasiconvex risk measures. By making use of the results on additively decomposable sums, we prove that natural quasiconvexity and convexity are exactly the same properties for conditional risk measures defined on Lp, for p ≥ 1, under some mild conditions. Lastly, we study naturally quasiconvex risk measures on L2 as a special case.
Open Access
Gain-loss pricing under ambiguity of measure
(E D P Sciences, 2010) Pınar, M. Ç.
Motivated by the observation that the gain-loss criterion, while offering economically meaningful prices of contingent claims, is sensitive to the reference measure governing the underlying stock price process (a situation referred to as ambiguity of measure), we propose a gain-loss pricing model robust to shifts in the reference measure. Using a dual representation property of polyhedral risk measures we obtain a one-step, gain-loss criterion based theorem of asset pricing under ambiguity of measure, and illustrate its use.
Open Access
Risk-averse control of undiscounted transient Markov models
(Society for Industrial and Applied Mathematics, 2014) Çavuş, Ö.; Ruszczyński, A.
We use Markov risk measures to formulate a risk-averse version of the undiscounted total cost problem for a transient controlled Markov process. Using the new concept of a multikernel, we derive conditions for a system to be risk transient, that is, to have finite risk over an infinite time horizon. We derive risk-averse dynamic programming equations satisfied by the optimal policy and we describe methods for solving these equations. We illustrate the results on an optimal stopping problem and an organ transplantation problem.