Applied Stochastic Control of Jump Diffusions

Øksendal, Bernt; Sulem, Agnès

doi:10.1007/978-3-540-69826-5

Cited by 735 publications

(786 citation statements)

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“…The result below comes from [13,Proposition 1] and is the solution of our problem, if there exists a function K(r) which solves (3.1) and satisfies (3.3). Its proof is based on the Hamilton-Jacobi-Bellman verification theorem (see [8,Theorem 3.1]) and is rather standard, so we give only a sketch of it. More information on stochastic control theory can be found, for example, in [3] and [10].…”

Section: Solution By the Hamilton-jacobi-bellman Verification Theoremmentioning

confidence: 99%

Optimal consumption problem in the Vasicek model

Trybuła

2015

OpMath

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Abstract. We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process. Using the method of subsolution and supersolution we obtain the existence of solutions of the dynamic programming equation. We illustrate the paper with a numerical example of the optimal consumption strategy and the value function.

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Section: Solution By the Hamilton-jacobi-bellman Verification Theoremmentioning

confidence: 99%

Optimal consumption problem in the Vasicek model

Trybuła

2015

OpMath

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“…This is the so-called 'bang-bang' property of stochastic control problems (Øksendal and Sulem 2005).…”

Section: Stochastic Modelmentioning

confidence: 99%

Valuation of energy storage: an optimal switching approach

Carmona

Ludkovski

2010

Quantitative Finance

146

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We consider the valuation of energy storage facilities within the framework of stochastic control. Our two main examples are natural gas dome storage and hydroelectric pumped storage. Focusing on the timing flexibility aspect of the problem we construct an optimal switching model with inventory. Thus, the manager has a constrained compound American option on the inter-temporal spread of the commodity prices.Extending the methodology from Carmona and Ludkovski (2008), we then construct a robust numerical scheme based on Monte Carlo regressions. Our simulation method can handle a generic Markovian price model and easily incorporates many operational features and constraints. To overcome the main challenge of the path-dependent storage levels two numerical approaches are proposed. The resulting scheme is compared to the traditional quasi-variational framework and illustrated with several concrete examples. We also consider related problems of interest, such as supply guarantees and mines management.Key words : gas storage; optimal switching; least squares Monte Carlo; hydro pumped storage; impulse control, commodity derivatives AcknowledgmentsWe thank the participants of the Banff BIRS Workshop 07w-5502 "Mathematics and the Environment" and Zhenwei J. Qin for many useful comments and discussions. We also thank the anonymous referees whose feedback led to much improved presentation.

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“…We refer to [9] for information about optimal stopping and stochastic control for jump diffusions. The following presentation follows [8] closely.…”

Section: General Formulationmentioning

confidence: 99%