Browsing by Subject "Mixed-integer programming"

Now showing 1 - 4 of 4

Open Access
Computation of systemic risk measures: a mixed-integer programming approach
(INFORMS Inst.for Operations Res.and the Management Sciences, 2023-09-22) Ararat, Çaǧın; Meimanjan, N.
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures have been proposed in the literature that are used to determine capital requirements for the members subject to joint risk considerations. We address the problem of computing systemic risk measures for systems with sophisticated clearing mechanisms. In particular, we consider an extension of the Rogers-Veraart network model where the operating cash flows are unrestricted in sign. We propose a mixed-integer programming problem that can be used to compute clearing vectors in this model. Because of the binary variables in this problem, the corresponding (set-valued) systemic risk measure fails to have convex values in general. We associate nonconvex vector optimization problems with the systemic risk measure and provide theoretical results related to the weighted-sum and Pascoletti-Serafini scalarizations of this problem. Finally, we test the proposed formulations on computational examples and perform sensitivity analyses with respect to some model-specific and structural parameters. Copyright: © 2023 INFORMS.
Open Access
Pricing multiple exercise American options by linear programming
(Springer New York LLC, 2017) Giandomenico, M.; Pınar, Mustafa Ç.
We consider the problem of computing the lower hedging price of American options of the call and put type written on a non-dividend paying stock in a non-recombinant tree model with multiple exercise rights. We prove using a simple argument that an optimal exercise policy for an option with h exercise rights is to delay exercise until the last h periods. The result implies that the mixedinteger programming model for computing the lower hedging price and the optimal exercise and hedging policy has a linear programming relaxation that is exact, i.e., the relaxation admits an optimal solution where all variables required to be integral have integer values. © Springer International Publishing Switzerland 2017.
Open Access
Risk-averse multi-stage mixed-integer stochastic programming problems
(2019-01) Mahmutoğulları, Ali İrfan
Risk-averse multi-stage mixed-integer stochastic programming problems form a class of extremely challenging problems since the problem size grows exponentially with the number of stages, they are non-convex due to integrality restrictions, and their objective functions are nonlinear in general. In this thesis, we first focus on such problems with an objective of dynamic mean conditional value-at-risk. We propose a scenario tree decomposition approach to obtain lower and upper bounds for their optimal values and then use these bounds in an evaluate-and-cut procedure which serves as an exact solution algorithm for such problems with integer first-stage decisions. Later, we consider a risk-averse day-ahead scheduling of electricity generation or unit commitment problem where the objective is a dynamic coherent risk measure. We consider two different versions of the problem: adaptive and non-adaptive. In the adaptive model, the commitment decisions are updated in each stage, whereas in the non-adaptive model, the commitment decisions are fixed in the first-stage. We provide theoretical and empirical analyses on the benefit of using an adaptive multi-stage stochastic model. Finally, we investigate the trade off between the adaptivity of the model and the computational effort to solve it for risk-averse multi-stage production planning problems with an objective of dynamic coherent risk measure. We also conduct computational experiments in order to verify the theoretical findings and discuss the results of these experiments.
Open Access
Robust auction design under multiple priors by linear and integer programming
(Springer New York LLC, 2018) Koçyiğit, Ç.; Bayrak, Halil İbrahim; Pınar, Mustafa Çelebi
It is commonly assumed in the optimal auction design literature that valuations of buyers are independently drawn from a unique distribution. In this paper we study auctions under ambiguity, that is, in an environment where valuation distribution is uncertain itself, and present a linear programming approach to robust auction design problem with a discrete type space. We develop an algorithm that gives the optimal solution to the problem under certain assumptions when the seller is ambiguity averse with a finite prior set P and the buyers are ambiguity neutral with a prior f∈ P. We also consider the case where all parties, the buyers and the seller, are ambiguity averse, and formulate this problem as a mixed integer programming problem. Then, we propose a hybrid algorithm that enables to compute an optimal solution for the problem in reduced time.