The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …

An optimization problem of controlling a dam installed in a river is analyzed based on a
stochastic control formalism of a diffusion process under model ambiguity: a new …

Nonsmooth dynamics driven by stochastic disturbance arise in a wide variety of engineering
problems. Impulsive interventions are often employed to control stochastic systems; …

We propose a tractable dynamic framework for the joint determination of optimal
consumption, portfolio choice, and healthcare irreversible investment. Our model is based …

Financial mathematics, an interdisciplinary subject between mathematics and finance, is the
application of mathematics in the financial field, which carries mainly out the quantitative …

The classical setting in optimal stopping and optimal control theory assumes that the agent
controlling the system can operate continuously in time. In optimal stopping this setting is …

We study a problem of optimal investment/consumption over an infinite horizon in a market
consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded …

We propose a tractable dynamic framework for the joint determination of optimal
consumption, portfolio choice, and healthcare irreversible investment. Our model is based …

This thesis investigates stochastic control models arising in insurance mathematics. From a
mathematical point of view, the models presented in Chapters 2-4 can be formulated as …

This paper considers a utility maximization and optimal asset allocation problem in the
presence of a stochastic endowment that cannot be fully hedged through trading in the …