Hedging of an option book in an incomplete market with transaction costs is an important problem in finance that many banks have to solve on a daily basis. In this paper, we develop a stochastic programming (SP) model...
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Hedging of an option book in an incomplete market with transaction costs is an important problem in finance that many banks have to solve on a daily basis. In this paper, we develop a stochastic programming (SP) model for the hedging problem in a realistic setting, where all transactions take place at observed bid and ask prices. The SP model relies on a realistic modeling of the important risk factors for the application, the price of the underlying security and the volatility surface. The volatility surface is unobservable and must be estimated from a cross section of observed option quotes that contain noise and possibly arbitrage. In order to produce arbitrage-free volatility surfaces of high quality as input to the SP model, a novel non-parametric estimation method is used. The dimension of the volatility surface is infinite and in order to be able solve the problem numerically, we use discretization and principal component analysis to reduce the dimensions of the problem. Testing the model out-of-sample for options on the Swedish OMXS30 index, we show that the SP model is able to produce a hedge that has both a lower realized risk and cost compared with dynamic delta and delta-vega hedging strategies.
The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multista...
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The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multistage stochastic programming problems in arborescent form (i.e. formulated with implicit non-anticipativity constraints on a scenario tree). The objective function of the problem can be either linear or nonlinear, while we require that the constraints are linear and involve only variables from two adjacent periods (current and lag 1). The approach is built on the following steps. First, reformulate the stochastic programming problem into an optimal control one. Second, apply a discrete version of Pontryagin maximum principle to obtain optimality conditions. Third, discuss and rearrange these conditions to obtain a decomposition that acts both at a time stage level and at a nodal level. To obtain the solution of the original problem we aggregate the solutions of subproblems through an enhanced mean valued fixed point iterative scheme.
We consider expected return, Conditional Value at Risk, and liquidity criteria in a multi-period portfolio optimization setting modeled by stochastic programming. We aim to identify a preferred solution of the decisio...
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We consider expected return, Conditional Value at Risk, and liquidity criteria in a multi-period portfolio optimization setting modeled by stochastic programming. We aim to identify a preferred solution of the decision maker (DM) by obtaining information on her/his preferences. We use a weighted Tchebycheff program to generate representative sets of solutions. Our approach models the stochasticity of market movements by stochastic programming. Working with multiple scenario trees, we construct confidence ellipsoids around representative solutions, and present them to the DM for her/him to make a choice. With each iteration of the approach, an increasingly concentrated set of ellipsoids around the DM's choices are generated. The procedure is demonstrated with tests performed using stocks traded on Borsa Istanbul.
In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchma...
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Integrating wind generation in power systems has raised the issue of optimal transmission access for generators. The available transmission capacity for a generator is now subject to the uncertain wind generation. The...
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Integrating wind generation in power systems has raised the issue of optimal transmission access for generators. The available transmission capacity for a generator is now subject to the uncertain wind generation. Therefore, the need for a transmission access mechanism has emerged. This study proposes three different optimisation models for calculating transmission access under uncertain wind generation. First, it develops a mathematical model to find the expected transmission access. A chance-constrained optimisation model is derived to find different levels of access to the transmission network with pre-specified reliability levels. The chance-constrained model provides detailed information regarding the available transmission access at different reliability levels. This gives options to a connecting generator regarding its choice of transmission access. Finally, a robust model for transmission access is proposed. The robust model provides the conservative transmission access which is assured against all future realisations of wind generation. The proposed expected, chance-constrained and robust approaches for optimal transmission access are numerically studied using an illustrative 2-bus example and the IEEE 30-bus and IEEE 300-bus case studies. The moment-matching technique is used to generate wind and demand scenarios. The numerical results show the utility of three derived models to calculate the optimal transmission access for generators.
To match products of different quality with end market preferences under supply uncertainty, it is crucial to integrate product quality information in logistics decision making. We present a case of this integration i...
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To match products of different quality with end market preferences under supply uncertainty, it is crucial to integrate product quality information in logistics decision making. We present a case of this integration in a meat processing company that faces uncertainty in delivered livestock quality. We develop a stochastic programming model that exploits historical product quality delivery data to produce slaughterhouse allocation plans with reduced levels of uncertainty in received livestock quality. The allocation plans generated by this model fulfil demand for multiple quality features at separate slaughterhouses under prescribed service levels while minimizing transportation costs. We test the model on real world problem instances generated from a data set provided by an industrial partner. Results show that historical farmer delivery data can be used to reduce uncertainty in quality of animals to be delivered to slaughterhouses.
The development of mobile cloud computing has brought many benefits to mobile users as well as cloud service providers. However, mobile cloud computing is facing some challenges, especially security-related problems d...
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We analyse how to deal with the uncertainty before solving a stochastic optimization problem and we apply it to a forestry management problem. In particular, we start from historical data to build a stochastic process...
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We analyse how to deal with the uncertainty before solving a stochastic optimization problem and we apply it to a forestry management problem. In particular, we start from historical data to build a stochastic process for wood prices and for bounds on its demand. Then, we generate scenario trees considering different numbers of scenarios and different scenario-generation methods, and we describe a procedure to compare the solutions obtained with each approach. Finally, we show that the scenario tree used to obtain a candidate solution has a considerable impact in our decision model.
In situations where risk aversion is involved, minimization of the variability of the economic criterion under consideration is indispensable. This paper provides a typical stochastic fractional programming model for ...
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In situations where risk aversion is involved, minimization of the variability of the economic criterion under consideration is indispensable. This paper provides a typical stochastic fractional programming model for minimizing the absolute value of the coefficient of variation of a linear function of decision variables under the assumption that the coefficient parameters of the decision variables have a known multivariate normal probability distribution. The stochastic problem is shown to be equivalent to a deterministic problem whose solution can be obtained by solving a related quadratic programming problem.
We address the problem of enhancing Quality-of-Service (QoS) in power constrained, mobile relay beamforming networks, by controlling the motion of the relaying nodes. We consider a time slotted system, where the relay...
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ISBN:
(纸本)9781509041183
We address the problem of enhancing Quality-of-Service (QoS) in power constrained, mobile relay beamforming networks, by controlling the motion of the relaying nodes. We consider a time slotted system, where the relays update their positions before the beginning of each time slot. Adopting a spatiotemporal stochastic field model of the wireless channel, we propose a novel 2-stage stochastic programming formulation for specifying the relay positions at each time slot, such that the QoS of the network is maximized on average, based on causal Channel State Information (CSI) and under a total relay transmit power budget. Via the Method of Statistical Differentials, the motion control problem considered is shown to be approximately equivalent to a set of simple subproblems, which are solved in a distributed fashion, one at each relay. Numerical simulations are also presented, corroborating the efficacy of the proposed approach.
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