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Controlling the stochastic dynamics of biological populations is a challenge that arises across various biological contexts. However, these dynamics are inherently nonlinear and involve a discrete state space, i.e., the number of molecules,…
We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian…
We introduce a dynamic optimization framework to analyze optimal portfolio allocations within an information driven contagious distress model. The investor allocates his wealth across several stocks whose growth rates and distress…
We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…
The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time…
Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…
We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving…
We present a continuous-time portfolio selection framework that reflects goal-based investment principles and mental accounting behavior. In this framework, an investor with multiple investment goals constructs separate portfolios, each…
We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
We address the problem of combined stochastic and impulse control for a market maker operating in a limit order book. The problem is formulated as a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose an implicit…
In this paper we study the optimization problem of an economic agent who chooses a job and the time of retirement as well as consumption and portfolio of assets. The agent is constrained in the ability to borrow against future income. We…
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…
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…
We formulate a continuous-time competitive equilibrium model of irreversible capacity investment in which a continuum of heterogeneous producers supplies a single non-durable good subject to exogenous stochastic demand. Each producer…
Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse optimality property since each passivating state feedback controller is optimal with respect to some specific performance index. Due to the nonlinear…
This study investigates an optimal investment problem for an insurance company operating under the Cramer-Lundberg risk model, where investments are made in both a risky asset and a risk-free asset. In contrast to other literature that…
Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…
This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be…