Related papers: Non-smooth analysis method in optimal investment- …
Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time…
We consider an optimal consumption/investment problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio which consists of one bond, one liquid risky asset (no transaction…
This thesis develops equilibrium asset pricing models in incomplete markets with a large number of heterogeneous agents using mean field game theory. The market equilibrium is characterized by a novel form of mean field backward stochastic…
This paper studies the continuous time mean-variance portfolio selection problem with one kind of non-linear wealth dynamics. To deal the expectation constraint, an auxiliary stochastic control problem is firstly solved by two new…
In this work we use an inelastic scattering process of particles to propose a model able to reproduce the salient features of the wealth distribution in an economy by including taxes to each trading process and redistributing that collected…
The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial…
The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally…
Motivated by the trade-off between exploitation and exploration in reinforcement learning, we study a continuous-time entropy-regularized mean variance portfolio selection problem in the presence of jumps. We propose an exploratory SDE for…
In this paper we study by probabilistic techniques the convergence of the value function for a two-scale, infinite-dimensional, stochastic controlled system as the ratio between the two evolution speeds diverges. The value function is…
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The…
Assume (1) asset returns follow a stochastic multi-factor process with time-varying conditional expectations; (2) investments are linear functions of factors. This paper calculates asymptotic joint moments of the logarithm of investor's…
To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain…
We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model…
Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In…
We study optimal stochastic control problem for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients, and gain functionals are path-dependent, and importantly we do not make any ellipticity…
This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration.…