arXiv subjects

Clarence Simard

Publications and source records attributed to Clarence Simard.

5 recordsLinked to original sources

arXiv2026

A new perspective on the L{\o}kka-Zervos dichotomy for absolutely continuous dividend strategies

We revisit the optimization problem (and its dichotomous solution) analyzed in Renaud et al. (2026). By choosing affine functions (of the surplus level) to bound the dividend rates, we are able to provide a more explicit derivation of the solution, avoiding the use of viscosity solutions. Moreover, with explicitly parameterized expressions, we are able to study analytical properties of the optimal thresholds and to refine the statement of the dichotomy. To reach these objectives, we add a penalty-at-ruin parameter in the performance function, allowing us to unify the expressions of the value functions of the two subproblems appearing in the dichotomous solution; as a by-product, the dichotomy can also be expressed in terms of this newly added parameter. Finally, we perform sensitivity analyses to illustrate that the range of values generated in an affine-bound framework is flexible and can span the range from a constant bound to the singular version of this problem.

math.OC↗

arXiv2024

Deep Hedging with Market Impact

Dynamic hedging is the practice of periodically transacting financial instruments to offset the risk caused by an investment or a liability. Dynamic hedging optimization can be framed as a sequential decision problem; thus, Reinforcement Learning (RL) models were recently proposed to tackle this task. However, existing RL works for hedging do not consider market impact caused by the finite liquidity of traded instruments. Integrating such feature can be crucial to achieve optimal performance when hedging options on stocks with limited liquidity. In this paper, we propose a novel general market impact dynamic hedging model based on Deep Reinforcement Learning (DRL) that considers several realistic features such as convex market impacts, and impact persistence through time. The optimal policy obtained from the DRL model is analysed using several option hedging simulations and compared to commonly used procedures such as delta hedging. Results show our DRL model behaves better in contexts of low liquidity by, among others: 1) learning the extent to which portfolio rebalancing actions should be dampened or delayed to avoid high costs, 2) factoring in the impact of features not considered by conventional approaches, such as previous hedging errors through the portfolio value, and the underlying asset's drift (i.e. the magnitude of its expected return).

q-fin.CP↗

arXiv2023

An optimization dichotomy for capital injections and absolutely continuous dividend strategies

We consider an optimal stochastic control problem in which a firm's cash/surplus process is controlled by dividend payments and capital injections. Stockholders aim to maximize their dividend stream minus the cost of injecting capital, if needed. We consider absolutely continuous dividend policies subject to a level-dependent upper bound on the dividend rate while we allow for general capital injections behavior. We prove that the optimal strategy can only be of two types: dividends are paid according to a \textit{mean-reverting} strategy with capital injections performed each time the cash process reaches zero; or, dividends are paid according to another \textit{mean-reverting} strategy and no injection of capital is ever made, until ruin is reached. We give a complete solution to this problem and characterize this dichotomy by comparing (the derivatives of) the value functions at zero of two sub-problems. The first sub-problem is concerned solely with the maximization of dividends, while the second sub-problem is the corresponding bail-out optimal dividend problem for which we provide also a complete solution.

math.OC↗

arXiv2020

A stochastic control problem with linearly bounded control rates in a Brownian model

Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a Brownian model, we prove the optimality of a member of a new family of control strategies called delayed linear control strategies, for which the controlled process is a refracted diffusion process. For some parameters specifications, we retrieve the strategy initially proposed by Avanzi & Wong (2012) to regularize dividend payments, which is more consistent with actual practice.

math.PR↗

arXiv2018

Martingale decomposition of a $L^2$ space with nonlinear stochastic integrals

This paper presents a generalization of the Kunita-Watanabe decomposition of a $L^2$ space with nonlinear stochastic integrals where the integrator is a family of continuous martingales bounded in $L^2$. To get the result, a useful relation between the regularity of the martingale family respect to its parameter and the regularity of the integrand in its martingale decomposition is shown.The decomposition presented in the main result is also the solution of an optimization problem in $L^2$. Finally, an example is given where the optimization problem is solved explicitely.

math.PR↗