Markowitz Portfolio Selection for Multivariate Affine and Quadratic Volterra Models

Jaber, Eduardo Abi; Miller, Enzo; Pham, Huyên

doi:10.2139/ssrn.3636794

Cited by 5 publications

(12 citation statements)

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“…In [19], the popular Heston model [18] was adapted to the rough volatility framework by using a fractional process with Hurst index H < 1 2 as driver of the volatility process. A more general class of volatility models covering the rough Heston model in [19] is obtained by modelling the volatility process as a stochastic Volterra equation of convolution type [1,20,5]. Although most of the literature about rough volatility is concerned with option pricing, there are some recent works dealing with Merton portfolio optimization in such models.…”

Section: Introductionmentioning

confidence: 99%

“…Although most of the literature about rough volatility is concerned with option pricing, there are some recent works dealing with Merton portfolio optimization in such models. While [10] and [5] are dealing with the Markowitz portfolio problem, the Merton portfolio problem is studied in [6,2,9].…”

Section: Introductionmentioning

confidence: 99%

“…[23], [24], [1]). In [5], Abi Jaber et al study the Markowitz portfolio problem for a class of multivariate affine Volterra models, that features correlation between the stocks and between a stock and its volatility.…”

Section: Introductionmentioning

confidence: 99%

“…The outline of the paper is as follows: Section 2 gives an overview of the calculus of convolutions and resolvents which is needed throughout the paper. In Section 3 we introduce a class of multivariate affine Volterra models studied in [1] and [5]. For such a market model we consider two different approaches to solve the Merton portfolio problem.…”

Section: Introductionmentioning

confidence: 99%

“…We first adapt the martingale distortion transformation used in [9] to the multivariate case. However, as it is pointed out in [5], this only works if the correlation structure is highly degenerate. Inspired by the techniques used in [3], we then provide a solution for the Merton portfolio problem for a more general correlation structure using calculus of convolutions and resolvents.…”

Section: Introductionmentioning

confidence: 99%

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Utility maximization in multivariate Volterra models

Aichinger¹,

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This paper is concerned with portfolio selection for an investor with power utility in multi-asset financial markets in a rough stochastic environment. We investigate Merton's portfolio problem for a class of multivariate affine Volterra models introduced in [5] and a Volterra-Wishart model based on the model described in [3], both covering the rough Heston model. Due to the non-Markovianity of the underlying processes the classical stochastic control approach can not be applied in this setting. To overcome this difficulty, we provide a verification argument inspired by [3] to show that an appropriate candidate is indeed the optimal portfolio strategy using calculus of convolutions and resolvents. The optimal strategy can then be expressed explicitly in terms of the solution of a multivariate Riccati-Volterra equation. This extends the results obtained by Han and Wong to the multivariate case, avoiding restrictions on the correlation structure linked to the martingale distortion transformation used in [9]. We also provide a numerical study to illustrate our results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Utility maximization in multivariate Volterra models

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Deep learning for efficient frontier calculation in finance

Warin¹

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We propose deep neural network algorithms to calculate efficient frontier in some Mean-Variance and Mean-CVaR portfolio optimization problems. We show that we are able to deal with such problems when both the dimension of the state and the dimension of the control are high. Adding some additional constraints, we compare different formulations and show that a new projected feedforward network is able to deal with some global constraints on the weights of the portfolio while outperforming classical penalization methods. All developed formulations are compared in between. Depending on the problem and its dimension, some formulations may be preferred.

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American options in the Volterra Heston model

Chevalier,

Pulido,

Zúñiga

2021

Preprint

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We price American options using kernel-based approximations of the Volterra Heston model. We choose these approximations because they allow simulation-based techniques for pricing. We prove the convergence of American option prices in the approximating sequence of models towards the prices in the Volterra Heston model. A crucial step in the proof is to exploit the affine structure of the model in order to establish explicit formulas and convergence results for the conditional Fourier-Laplace transform of the log price and an adjusted version of the forward variance. We illustrate with numerical examples our convergence result and the behavior of American option prices with respect to certain parameters of the model.

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Markowitz Portfolio Selection for Multivariate Affine and Quadratic Volterra Models

Cited by 5 publications

References 0 publications

Utility maximization in multivariate Volterra models

Utility maximization in multivariate Volterra models

Deep learning for efficient frontier calculation in finance

American options in the Volterra Heston model

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