Browsing by Subject "Dynamic risk measure"

Now showing 1 - 3 of 3

Open Access
Computational methods for risk-averse undiscounted transient markov models
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2014) Çavuş, O.; Ruszczyński, A.
The total cost problem for discrete-time controlled transient Markov models is considered. The objective functional is a Markov dynamic risk measure of the total cost. Two solution methods, value and policy iteration, are proposed, and their convergence is analyzed. In the policy iteration method, we propose two algorithms for policy evaluation: the nonsmooth Newton method and convex programming, and we prove their convergence. The results are illustrated on a credit limit control problem.
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.
Open Access
Set-valued risk measures as backward stochastic difference inclusions and equations
(Springer, 2021-01) Ararat, Çağın; Feinstein, Z.
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented via backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensions of scalar backward stochastic differential equations for the set-valued framework: (1) backward stochastic differential inclusions, which evaluate the risk dynamics on the selectors of acceptable capital allocations; or (2) set-valued backward stochastic differential equations, which evaluate the risk dynamics on the full set of acceptable capital allocations as a singular object. In this work, the discrete-time setting is investigated with difference inclusions and difference equations in order to provide insights for such differential representations for set-valued dynamic risk measures in continuous time.