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We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize…
We consider stochastic PDEs \[dY_t = L(Y_t)\, dt + A(Y_t).\, dB_t, t > 0\] and associated PDEs \[du_t = L u_t\, dt, t > 0\] with regular initial conditions. Here, $L$ and $A$ are certain partial differential operators involving…
In this paper we investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in finance when we want to find an investment strategy and an…
Predictable forward performance processes (PFPPs) are stochastic optimal control frameworks for an agent who controls a randomly evolving system but can only prescribe the system dynamics for a short period ahead. This is a common scenario…
This thesis develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time finance, does not rely on stochastic integrals or other probabilistic…
We study the forward investment performance process (FIPP) in an incomplete semimartingale market model with closed and convex portfolio constraints, when the investor's risk preferences are of the power form. We provide necessary and…
This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log…
We study backward stochastic difference equations (BS{\Delta}E) driven by a d-dimensional stochastic process on a lattice whose increments have only d + 1 possible values that generates the lattice. Regarding the driving process as a d…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…
Linear-quadratic optimal control problem for systems governed by forward-backward stochastic differential equations has been extensively studied over the past three decades. Recent research has revealed that for forward-backward control…
We study the optimal investment and proportional reinsurance problem of an insurance company, whose investment preferences are described via a forward dynamic utility of exponential type in a stochastic factor model allowing for a possible…
Recent developments on financial markets have revealed the limits of Brownian motion pricing models when they are applied to actual markets. L\'evy processes, that admit jumps over time, have been found more useful for applications. Thus,…
We consider the following problem in stochastic portfolio theory. Are there portfolios that are relative arbitrages with respect to the market portfolio over very short periods of time under realistic assumptions? We answer a slightly…
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…
In this paper, a class of non-Markovian forward-backward doubly stochastic systems is studied. By using the technique of functional It\^o (or path-dependent) calculus, the relationship between the systems and related path-dependent…
We consider the Cauchy problem for a linear stochastic partial differential equation. By extending the parametrix method for PDEs whose coefficients are only measurable with respect to the time variable, we prove existence, regularity in…
Optimal investment strategies of an individual worker during the accumulation phase in the defined contribution pension scheme have been well studied in the literature. Most of them adopted the classical backward model and approach, but any…
We address a portfolio selection problem that combines active (outperformance) and passive (tracking) objectives using techniques from convex analysis. We assume a general semimartingale market model where the assets' growth rate processes…
The solution to a stochastic optimal control problem can be determined by computing the value function from a discretization of the associated Hamilton-Jacobi-Bellman equation. Alternatively, the problem can be reformulated in terms of a…