Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance

Framstad, Nils Christian; Øksendal, Bernt; Sulem, Agnès

doi:10.1023/b:jota.0000026132.62934.96

Cited by 137 publications

(103 citation statements)

References 14 publications

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“…In order to verify the correctness of our guess, we use the stochastic maximum principle proposed by Framstad et al (2004) to show that the policy rule identified in (29) is optimal. By defining m t ≡ ∂J /∂ p and n t ≡ ∂ 2 J /∂ p 2 , it is possible to rewrite (20) as:…”

Section: Appendix 1: Optimal Solution and Sufficiencymentioning

confidence: 99%

“…Theorem 2.1 of Framstad et al (2004) states that, for an admissible set of state and controls, if the minimized HamiltonianĤ (that is the Hamiltonian H evaluated at the value of the optimal control τ * ) is convex in p for all t in [0, t], then the pair (τ * , p) represents an optimal pair for the problem. Note that H is strictly convex in τ since ∂ 2 H/∂τ 2 = p 2 e −ρt > 0.…”

Section: Appendix 1: Optimal Solution and Sufficiencymentioning

confidence: 99%

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Pollution Control Under Uncertainty and Sustainability Concern

Torre

Liuzzi

Marsiglio

2016

Environ Resource Econ

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We analyze the implications of environmental policy on pollution in a stochastic framework with finite horizon and sustainability concern. The social planner seeks to minimize the social (environmental and economic) costs associated with pollution. We allow for the planner to attach different relative weights to the discounted and end-of-planning-horizon costs in order to assess how sustainability concern might affect the optimal level of policy intervention. We show that the optimal environmental policy increases with the degree of sustainability concern, reducing thus the amount of pollution the society is forced to bear. A calibration based on world CO 2 data supports our conclusions, further highlighting the importance of higher degrees of sustainability concern to achieve greener long run outcomes. It also allows us to show that under a realistic model's parametrization the optimal environmental policy tends to rise with higher degrees of uncertainty in a precautionary manner.

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Section: Appendix 1: Optimal Solution and Sufficiencymentioning

confidence: 99%

Section: Appendix 1: Optimal Solution and Sufficiencymentioning

confidence: 99%

Pollution Control Under Uncertainty and Sustainability Concern

Torre

Liuzzi

Marsiglio

2016

Environ Resource Econ

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“…Under the above jump-diffusion framework, Framstad, et al [13] discussed the mean-variance portfolio selection problem in Example 3.1, that is, the investor's object is to find an admissible portfolio v * (t) which minimizes the variance…”

Section: Applications To Financementioning

confidence: 99%

Maximum principle for forward-backward stochastic control system with random jumps and applications to finance

Shi

2010

J Syst Sci Complex

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Both necessary and sufficient maximum principles for optimal control of stochastic system with random jumps consisting of forward and backward state variables are proved. The control variable is allowed to enter both diffusion and jump coefficients. The result is applied to a mean-variance portfolio selection mixed with a recursive utility functional optimization problem. Explicit expression of the optimal portfolio selection strategy is obtained in the state feedback form.

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“…We refer to Chapter 1 of [22] for more detailed discussions on the price behavior which shows that discontinuity and jumps are common in the market. Meanwhile, more and more scholars use (exponential) Lévy processes to describe price processes, see, for example, [23][24][25][26]. In addition, this paper adopts the stochastic dynamic programming and the duality theory, while [17][18][19] used the LQ control method.…”

Section: Introductionmentioning

confidence: 99%

Asset-liability management under benchmark and mean-variance criteria in a jump diffusion market

Zeng

2011

J Syst Sci Complex

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This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the risky asset's price is governed by an exponential Lévy process, the liability evolves according to a Lévy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.

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Sufficient Stochastic Maximum Principle for the Optimal Control of Jump Diffusions and Applications to Finance

Abstract: We give a verification theorem by employing Arrow's generalization of the Mangasarian sufficient condition to a general jump diffusion setting, and show the adjoint processes' connections to dynamic programming. The result is applied to financial optimization problems.

Cited by 137 publications

References 14 publications

Pollution Control Under Uncertainty and Sustainability Concern

Pollution Control Under Uncertainty and Sustainability Concern

Maximum principle for forward-backward stochastic control system with random jumps and applications to finance

Asset-liability management under benchmark and mean-variance criteria in a jump diffusion market

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