Simulation methods for stochastic storage problems: a statistical learning perspective

Ludkovski, Michael; Maheshwari, Aditya

doi:10.1007/s12667-018-0318-4

Cited by 13 publications

(9 citation statements)

References 37 publications

(136 reference statements)

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“…However, it is not well-suited to solve numerically general control problems in dimension greater than 1. For these cases, other interpolating methods such as the use of Gaussian processes are more appropriated (see, e.g., [18] for an introduction on the use of Gaussian processes in Regression Monte Carlo).…”

Section: Piecewise Constant Interpolationmentioning

confidence: 99%

A class of finite-dimensional numerically solvable McKean-Vlasov control problems

et al. 2019

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We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stochastic control problems, and provide a discussion and comparison of three probabilistic numerical methods for solving the reduced control problem: quantization, regression by control randomization, and regress-later methods. Our numerical results are illustrated on various examples from portfolio selection and liquidation under drift uncertainty, and a model of interbank systemic risk with partial observation.

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Section: Piecewise Constant Interpolationmentioning

confidence: 99%

A class of finite-dimensional numerically solvable McKean-Vlasov control problems

et al. 2019

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“…In the case of controlled dynamics, Kharroubi et al (2015) analyzed the time-discretization error, and Kharroubi et al (2014) investigated the projection error generated by approximating the conditional expectation by basis functions for the control randomization scheme. Recently, alternative randomization schemes have been proposed in the literature, such as Ludkovski and Maheshwari (2019), Balata and Palczewski (2018), Bachouch et al (2018) or Shen and Weng (2019), which are more amenable to comprehensive convergence proofs, see Balata and Palczewski (2017) and Huré et al (2018). Nevertheless, the classical control randomization scheme retains some unique advantages, such as the ease with which it can handle switching costs, as shown in Zhang et al (2019).…”

Section: Control Randomizationmentioning

confidence: 99%

Robust utility maximization under model uncertainty via a penalization approach

Guo,

Langrené,

Loeper

et al. 2019

Preprint

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This article considers the problem of utility maximization with an uncertain covariance matrix. In contrast with the classical uncertain parameter approach, where the parameters of the model evolve within a given range, we constrain them by penalization. We show that this robust optimization process can be interpreted as a two-player zero-sum stochastic differential game. We prove that the value function satisfies the Dynamic Programming Principle and that it is the unique viscosity solution of an associated Hamilton-Jacobi-Bellman-Isaacs equation. We derive an analytical solution in the logarithmic utility case and obtain accurate numerical approximations in the general case by two methods: finite differences and Monte Carlo simulation.

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“…It is also possible to use global polynomials in regressions as in Longstaff and Schwartz (2001) or to use kernel regression methods as in the recent paper Langrené and Warin (2017). A recent comparison of some regression techniques to value some gas storages can be found in Ludkovski and Maheshwari (2018).…”

Section: Effective Implementation Based On Local Regressionsmentioning

confidence: 99%

Variance optimal hedging with application to electricity markets

Warin¹

2019

JCF

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In this article, we use the mean variance hedging criterion to value contracts in incomplete markets. Although the problem is well studied in a continuous and even discrete framework, very few works incorporating illiquidity constraints have been achieved and no algorithm is available in the literature to solve this problem. We first show that the valuation problem incorporating illiquidity constraints with a mean variance criterion admits a unique solution. Then we develop two Least Squares Monte Carlo algorithms based on the dynamic programming principle to efficiently value these contracts: in these methods, conditional expectations are classically calculated by regression using a dynamic programming approach discretizing the control. The first algorithm calculates the optimal value function while the second calculates the optimal cash flow generated along the trajectories. In a third part, we give the example of the valuation of a load curve contract coming from energy markets. In such contracts, incompleteness comes from the uncertainty of the customer's load that cannot be hedged and very tight illiquity constraints are present. We compare strategies given by the two algorithms and by some closed formula ignoring constraints and we show that hedging strategies can be very different. A numerical study of the convergence of the algorithms is also given.

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Simulation methods for stochastic storage problems: a statistical learning perspective

Cited by 13 publications

References 37 publications

A class of finite-dimensional numerically solvable McKean-Vlasov control problems

A class of finite-dimensional numerically solvable McKean-Vlasov control problems

Robust utility maximization under model uncertainty via a penalization approach

Variance optimal hedging with application to electricity markets

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