arXiv subjects

Sigui Brice Dro

Publications and source records attributed to Sigui Brice Dro.

4 recordsLinked to original sources

arXiv2026

Optimal Merton's Problem under Multivariate Affine Volterra Models with Jumps

This paper is concerned with portfolio selection for an investor with exponential, power, and logarithmic utility in multi-asset financial markets allowing jumps. We investigate the classical Merton's portfolio optimization problem in a Volterra stochastic environment described by a multivariate Volterra--Heston model with jumps driven by an independent Poisson random measure. Owing to the non-Markovian and non-semimartingale nature of the model, classical stochastic control techniques are not directly applicable. Instead, the problem is tackled using the martingale optimality principle by constructing a family of supermartingale processes characterized via solutions to an original Riccati backward stochastic differential equation with jumps (Riccati BSDEJ).The resulting optimal strategies for Merton's problems, as well as the corresponding indifference prices, are derived in semi-closed form depending on the solutions to time-dependent multivariate Riccati-Volterra integral equations with Lévy exponential jump compensator, while the optimal value is expressed using the solution to this original Riccati BSDEJ. Numerical experiments on a two-dimensional rough Heston model illustrate the impact of both path roughness and jumps components on the value function and optimal strategies in the Merton problem.

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arXiv2026

On explicit solutions to a class of quadratic BSDEJs driven by affine Volterra processes with jumps and applications

In this paper we consider a class of quadratic BSDEs with jumps (quadratic BSDEJs) involving inhomogeneous affine Volterra processes and show that their solution can be reduced to solving a system of generalized inhomogeneous integral Riccati-Volterra ordinary differential equations with Lévy jump compensators. This yields a rich and flexible class of quadratic BSDEJs that are analytically tractable, in the sense that their solutions are explicit up to the solution of an associated integral Riccati-Volterra ODE with Lévy jump compensator. As an application, we provide analytically tractable solutions to the continuous-time Markowitz mean-variance portfolio selection problem within a multivariate class of affine Volterra models allowing jumps driven by an independent Poisson random measure. In this non-Markovian and non-semimartingale market framework with unbounded random coefficients, the classical stochastic control approach cannot be directly applied to the associated optimization task. Instead, the problem is tackled using the martingale optimality principle by constructing a family of submartingale processes characterized via solutions to a novel Riccati backward stochastic differential equation with jumps (Riccati BSDEJ), particular subclass of the aforementionned quadratic BSDEJ. Specifically, we obtain analytical closed-form expressions for the optimal feedback control as well as the mean-variance efficient frontier, both of which depend on the solution to the associated multivariate inhomogeneous Riccati-Volterra system, while the optimal value function is expressed using the solution to this original Riccati BSDEJ. Furthermore, numerical experiments on a two-dimensional fake stationary rough Heston model is discussed and used to highlight the impact of stabilized rough volatilities on the Markowitz allocation problem.

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arXiv2026

Multi-Asset Utility Maximization with Jump Signals

In this paper, we study portfolio utility maximization problem in a setting where the risky asset is driven by a multidimensional Brownian motion and an independent homogeneous Poisson random measure, and where strategies may incorporate jump signals. Following the same approach as in the one-dimensional case for the exponential utility function [17], we first represent the portfolio dynamics as semimartingale processes. We then use martingale optimality principle to derive the corresponding backward stochastic differential equation (BSDE) with jumps to characterize both value function and an optimal strategy in terms of its solution. We subsequently prove the existence and uniqueness of the solution to the related BSDE with jumps. We also address the idiosyncratic case i.e where the investor receive heterogeneous jump signals. Finally, we provide numerical illustrations with Gaussian signals for the logarithmic case.

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arXiv2026

Portfolio Exponential Utility Maximization with Jump Signals

In this paper, we study the portfolio utility maximization in the case where the risky asset is driven by a Brownian motion and an independent homogeneous Poisson measure, with strategies that may include jump signals. This means that the allowed strategies are no longer predictable but also include the information given by a process driven by the Poisson measure. Using the results of Bank and K{ö}rber [1], we first express the considered portfolio as semi-martingale processes. We then present the martingale optimality principle for the exponential utility maximization. This allows to derive an original BSDE with jumps and to express the optimal value and an optimal strategy using the solution to this original BSDE. We then prove existence of a solution to the considered BSDE. We finally present some numerical experiments to quantify the gain of utility given by the information from the jump signals.

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