arXiv subjects

Olivier Menoukeu Pamen

Publications and source records attributed to Olivier Menoukeu Pamen.

18 recordsLinked to original sources

arXiv2026

Quantifying socio-temporal effects of loan delinquency drivers in microfinance

We develop and evaluate a family of discrete-time logit-link (LLink) models, including fixed-effects and frailty extensions, to quantify associations between socio-temporal factors and loan delinquency transitions while accounting for latent borrower heterogeneity. Using monthly records for 1,716 borrowers from a Ghanaian microfinance institution, we model transitions among good, intermediate, and poor repayment states, distinguishing deterioration, persistence, and recovery. The Eid season and long vacation indicators are associated with repayment behaviour, although the magnitude and direction of their estimated effects vary across transitions. Bootstrap tests indicate residual borrower heterogeneity in recovery and persistent poor repayment but provide little support for time-dependent frailty beyond a random intercept. Random Forest and KTBoost perform better for several binary transitions, while the LLink models provide a transparent framework for estimating covariate effects and borrower heterogeneity. For multistate prediction, we propose an Optimised Matthews Correlation Coefficient (OMCC) rule and compare it with the Djeundje and Crook (D\&C) rule. The estimated socio-temporal effects are interpreted as conditional associations rather than causal effects.

q-fin.RM↗

arXiv2026

Stochastic Optimal Control for Systems with Drifts of Bounded Variation: A Maximum Principle Approach

We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and Borel measurable, $b_2$ has bounded variation, and $b_3$ is bounded and smooth. Under these minimal regularity assumptions, we establish a Pontryagin-type stochastic maximum principle. The analysis relies on new results for SDEs with random drift of bounded variation, including existence, uniqueness, and Malliavin-Sobolev differentiability of the state process. A key ingredient is an explicit representation of the first variation process obtained via integration with respect to the space-time local time of bounded variation processes. By combining a suitable approximation scheme with Ekeland's variational principle, and using a Garcia-Rodemich-Rumsey inequality to obtain a uniform control of the first variation, we derive the maximum principle. As an application, we derive an optimal corridor-type capital adjustment policy for an insurance surplus model.

math.OC↗

arXiv2025

Smoothness of solutions of hyperbolic stochastic partial differential equations with $L^{\infty}$-vector fields

In this paper we are interested in a quasi-linear hyperbolic stochastic differential equation (HSPDE) when the vector field is merely bounded and measurable. Although the deterministic counterpart of such equation may be ill-posed (in the sense that uniqueness or even existence might not be valid), we show for the first time that the corresponding HSPDE has a unique (Malliavin differentiable) strong solution. Our approach for proving this result rests on: 1) tools from Malliavin calculus and 2) variational techniques introduced in [Davie, Int. Math. Res. Not., Vol. 2007] non trivially extended to the case of SDEs in the plane by using an algorithm for the selection of certain rectangles. As a by product, we also obtain the Sobolev differentiability of the solution with respect to its initial value. The results derived here constitute a significant improvement of those in the current literature on SDEs on the plane and can be regarded as an analogous equivalent of the pioneering works by [Zvonkin, Math. URSS Sbornik, 22:129-149] and [Veretennikov, Theory Probab. Appl., 24:354-366] in the case of one-parameter SDEs with singular drift.

math.PR↗

arXiv2025

Strong solutions of fractional Brownian sheet driven SDEs with integrable drift

We prove the existence of a unique Malliavin differentiable strong solution to a stochastic differential equation on the plane with merely integrable coefficients driven by the fractional Brownian sheet with Hurst parameters less than 1/2. The proof of this result relies on a compactness criterion for square integrable Wiener functionals from Malliavin calculus ([Da Prato, Malliavin and Nualart, 1992]), variational techniques developed in the case of fractional Brownian motion ([Baños, Nielssen, and Proske, 2020]) and the concept of sectorial local nondeterminism (introduced in [Khoshnevisan and Xiao, 2007]). The latter concept enable us to improve the bound of the Hurst parameter (compare with [Baños, Nielssen, and Proske, 2020]).

math.PR↗

arXiv2024

Time discretization of Quadratic Forward-Backward SDEs with singular drifts

We investigate the convergence rate for the time discretization of a class of quadratic backward SDEs -- potentially involving path-dependent terminal values -- when coupled with non-standard Lipschitz-type forward SDEs. In our review of the explicit time-discretization schemes in the spirit of Pagès \& Sagna (see \cite{PaSa18}), we achieve an error control close to $\frac{1}{2}$, even under the modest assumptions considered in this work (see \cite{ChaRichou16}, for comparison). A central element of our approach is a thorough re-examination of Zhang's $L^2\text{-time regularity}$ of the martingale integrand $Z$ which follows from an extension of the first-order variational regularity for this class of singular forward-backward SDEs with non-uniform Cauchy-Lipschitz drivers. This is complemented by the recently introduced caracterisation of stochastic processes of {\it bounded mean oscillation} (abbreviated as $\bmo$) by K. Lê (see \cite{Le22}) which we used to derive an $L^p\text{-version}$ of the strong approximation of SDEs with singular drifts from Dareiotis \& Gerencsér (see \cite{DaGe20}). As such, this study addresses a crucial gap in the numerical analysis of forward-backward SDEs (FBSDEs). To our knowledge, for the first time, the impact of regularization by noise on Euler-Maruyama numerical schemes for singular forward SDEs has been successfully transferred to enhance the convergence rate of the discrete time approximations for solutions to backward SDEs.

math.PR↗

arXiv2024

On the valuation of life insurance policies for dependent coupled lives

In this paper, we investigate a complex variation of the standard joint life annuity policy by introducing three distinct contingent benefits for the surviving member(s) of a couple, along with a contingent benefit for their beneficiaries if both members pass away. Our objective is to price this innovative insurance policy and analyse its sensitivity to key model parameters, particularly those related to the joint mortality framework. We employ the $QP$-rule (described in Section \ref{secgenset}), which combines the real-world probability measure $P$ for mortality risk with risk-neutral valuation under $Q$ for financial market risks. The model enables explicit pricing expressions, computed using efficient numerical methods. Our results highlight the interdependent risks faced by couples, such as broken-heart syndrome, providing valuable insights for insurers and policyholders regarding the pricing influences of these factors.

q-fin.PR↗

arXiv2024

Density Analysis for coupled forward-backward SDEs with non-Lipschitz drifts and Applications

We explore the existence of a continuous marginal law with respect to the Lebesgue measure for each component $(X,Y,Z)$ of the solution to coupled quadratic forward-backward stochastic differential equations (QFBSDEs) {for which the drift coefficient of the forward component is either bounded and measurable or Hölder continuous. Our approach relies on a combination of the existence of a weak {\it decoupling field} (see \cite{Delarue2}), the integration with respect to space time local time (see \cite{Ein2006}), the analysis of the backward Kolmogorov equation associated to the forward component along with an Itô-Tanaka trick (see \cite{FlanGubiPrio10})}. The framework of this paper is beyond all existing papers on density analysis for Markovian BSDEs and constitutes a major refinement of the existing results. We also derive a comonotonicity theorem for the control variable in this frame and thus extending the works \cite{ChenKulWei05}, \cite{DosDos13}. As applications of our results, we first analyse the regularity of densities of solution to coupled FBSDEs. In the second example, we consider a regime switching term structure interest rate models (see for e.g., \cite{ChenMaYin17}) for which the corresponding FBSDE has discontinuous drift. Our results enables us to: firstly study classical and Malliavin differentiability of the solutions for such models, secondly the existence of density of such solutions. Lastly we consider a pricing and hedging problem of contingent claims on non-tradable underlying, when the dynamic of the latter is given by a regime switching SDE (i.e., the drift coefficient is allowed to be discontinuous). We obtain a representation of the derivative hedge as the weak derivative of the indifference price function, thus extending the result in \cite{ArImDR10}.

math.PR↗

arXiv2023

Short-Term Behavior of a Geothermal Energy Storage: Modeling and Theoretical Results

This paper investigates numerical methods for simulations of the short-term behavior of a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. There a given volume under or aside of a building is filled with soil and insulated to the surrounding ground. The thermal energy is stored by raising the temperature of the soil inside the storage. It is charged and discharged via pipe heat exchangers filled with a moving fluid. Simulations of geothermal energy storages aim to determine how much energy can be stored in or taken from the storage within a given short period of time. The latter depends on the dynamics of the spatial temperature distribution in the storage which is governed by a linear heat equation with convection and appropriate boundary and interface conditions. We consider semi- and full discretization of that PDE using finite difference schemes and study associated stability problems. Numerical results based on the derived methods are presented in the companion paper [17].

math.NA↗

arXiv2023

Short-Term Behavior of a Geothermal Energy Storage: Numerical Applications

This paper is devoted to numerical simulations of the short-term behavior of the spatial temperature distribution in a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. We apply numerical methods derived in our companion paper [15] in which we study the governing initial boundary value problem for a linear heat equation with convection. Further, we perform extensive numerical experiments in order to investigate properties of the spatio-temporal temperature distribution and of its aggregated characteristics.

math.NA↗

arXiv2022

Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts

We prove path-by-path uniqueness of solution to hyperbolic stochastic partial differential equations when the drift coefficient is the difference of two componentwise monotone Borel measurable functions of spatial linear growth. The Yamada-Watanabe principle for SDE driven by Brownian sheet then allows to derive strong uniqueness for such equation and thus extending the results in [Bogso, Dieye and Menoukeu Pamen, Elect. J. Probab., 27:1-26, 2022] and [Nualart and Tindel, Potential Anal., 7(3):661--680, 1997]. Assuming that the drift is globally bounded, we show that the unique strong solution is Malliavin differentiable. The case of spatial linear growth drift coefficient is also studied.

math.PR↗

arXiv2022

Stochastic integration with respect to local time of the Brownian sheet and regularising properties of Brownian sheet paths

In this work, we generalise the stochastic local time space integration introduced in \cite{Ei00} to the case of Brownian sheet. %We develop a stochastic local time-space calculus with respect to the Brownian sheet. This allows us to prove a generalised two-parameter Itô formula and derive Davie type inequalities for the Brownian sheet. Such estimates are useful to obtain regularity bounds for some averaging type operators along Brownian sheet curves.

math.PR↗

arXiv2022

Differentiability of quadratic forward-backward SDEs with rough drift

In this paper, we consider quadratic forward-backward SDEs (QFBSDEs), for {which} the drift in the forward equation does not satisfy the standard globally Lipschitz condition and the driver of the backward system {possesses} nonlinearity of type $f(|y|)|z|^2,$ where $f$ is any locally integrable function. We prove both the Malliavin and classical derivative of the QFBSDE and provide representations of these processes. We study a numerical approximation of this system in the sense of \cite{ImkDosReis} in which the authors assume that the drift is Lipschitz and the driver of the BSDE is quadratic in the traditional sense (i.e., $f$ is a positive constant). We show that the rate of convergence is the same as in \cite{ImkDosReis}

math.PR↗

arXiv2021

Rough Weierstrass functions and dynamical systems: the smoothness of the SBR measure

We investigate Weierstrass functions with roughness parameter $γ$ that are Hölder continuous with coefficient $H={\logγ}/{\log \frac12}.$ Analytical access is provided by an embedding into a dynamical system related to the baker transform where the graphs of the functions are identified as their global attractors. They possess stable manifolds hosting Sinai-Bowen-Ruelle (SBR) measures. We systematically exploit a telescoping property of associated measures to give an alternative proof of the absolute continuity of the SBR measure for large enough $γ$ with square-integrable density. Telescoping allows a macroscopic argument using the transversality of the flow related to the mapping describing the stable manifold. The smoothness of the SBR measure can be used to compute the Hausdorff dimension of the graphs of the original Weierstrass functions and investigate their local times.

math.DS↗

arXiv2017

Flows for Singular Stochastic Differential Equations with Unbounded Drifts

In this paper, we are interested in the following singular stochastic differential equation (SDE) $${\rm d} X_t = b(t,X_t) {\rm d} t + {\rm d} B_{t},\ 0\leq t\leq T,\ X_0 = x \in \mathbb{R}^d,$$ where the drift coefficient $b:[0,T]\times \mathbb{R}^{d}\longrightarrow \mathbb{R}^{d}$ is Borel measurable, possibly unbounded and has spatial linear growth. The driving noise $B_{t}$ is a $d-$ dimensional Brownian motion. The main objective of the paper is to establish the existence and uniqueness of a strong solution and a Sobolev differentiable stochastic flow for the above SDE. Malliavin differentiability of the solution is also obtained (cf.\cite{MMNPZ13, MNP2015}). Our results constitute significant extensions to those in \cite{Zvon74, Ver79, KR05, MMNPZ13, MNP2015} by allowing the drift $b$ to be unbounded. We employ methods from white-noise analysis and the Malliavin calculus. As application, we prove existence of a unique strong Malliavin differentiable solution to the following stochastic delay differential equation $${\rm d} X (t) = b (X(t-r), X(t,0,(v,η)) {\rm d} t + {\rm d} B(t), \,t \geq 0 ,\textbf{ } (X(0), X_0)= (v, η) \in \mathbb{R}^d \times L^2 ([-r,0], \mathbb{R}^d),$$ with the drift coefficient $b: \mathbb{R}^d \times \mathbb{R}^d \rightarrow \mathbb{R}^d$ is a Borel-measurable function bounded in the first argument and has linear growth in the second argument.

math.PR↗

arXiv2016

Strong rate of convergence for the Euler-Maruyama approximation of SDEs with Hölder continuous drift coefficient

In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) $$X_{t}=x_{0}+ \int_{0}^{t} b(s, X_{s}) \mathrm{d}s + L_{t},~x_{0} \in \mathbb{R}^{d},~t \in [0,T],$$ where the drift coefficient $b:[0,T] \times \mathbb{R}^d \to \mathbb{R}^d$ is Hölder continuous in both time and space variables and the noise $L=(L_t)_{0 \leq t \leq T}$ is a $d$-dimensional Lévy process. We provide the rate of convergence for the Euler-Maruyama approximation when $L$ is a Wiener process or a truncated symmetric $α$-stable process with $α\in (1,2)$. Our technique is based on the regularity of the solution to the associated Kolmogorov equation.

math.PR↗

arXiv2014

A Maximum Principle for Markov Regime-Switching Forward Backward Stochastic Differential Games and Applications

In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps and partial information. First, we prove a sufficient maximum principle for non zero-sum stochastic differential game problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for non zero-sum stochastic differential games. The zero-sum stochastic differential games equivalent maximum principle is then obtained as a corollary. We apply the obtained results to study a problem of robust utility maximization under penalty entropy. We also apply the result to find optimal investment of an insurance firm under model uncertainty.

math.OC↗

arXiv2014

Maximum Principles of Markov Regime-Switching Forward-Backward Stochastic Differential Equations with Jumps and Partial Information

This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward-backward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for optimal control for a system driven by a Markov regime-switching forward and backward jump-diffusion model is developed. After, an equivalent maximum principle is proved. Malliavin calculus is also employed to derive a general stochastic maximum principle. The latter does not require concavity of Hamiltonian. Applications of the stochastic maximum principle to non-concave Hamiltonian and recursive utility maximization is also discussed.

math.OC↗

arXiv2008

Decomposition of order statistics of semimartingales using local times

In a recent work \cite{BG}, given a collection of continuous semimartingales, authors derive a semimartingale decomposition from the corresponding ranked processes in the case that the ranked processes can meet more than two original processes at the same time. This has led to a more general decomposition of ranked processes. In this paper, we derive a more general result for semimartingales (not necessarily continuous) using a simpler approach. Furthermore, we also give a generalization of Ouknine \cite{O1, O2} and Yan's \cite{Y1} formula for local times of ranked processes

math.PR↗