Related papers: Some Computations for Optimal Execution with Monot…
We study a constrained stochastic control problem with jumps; the jump times of the controlled process are given by a Poisson process. The cost functional comprises quadratic components for an absolutely continuous control and the…
The classical optimal trading problem is the closure of a position in an asset over a time interval; the trader maximizes an expected utility under the constraint that the position be fully closed by terminal time. Since the asset price is…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a…
We use one-step conditional risk mappings to formulate a risk averse version of a total cost problem on a controlled Markov process in discrete time infinite horizon. The nonnegative one step costs are assumed to be lower semi-continuous…
We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in…
We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We give explicit solutions for investors with exponential, logarithmic and power utility.…
A linear control system with quadratic cost functional over infinite time horizon is considered without assuming controllability/stabilizability condition and the global integrability condition for the nonhomogeneous term of the state…
We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the…
This paper deals with an optimal position management problem for a market maker who has to face uncertain customer order flows in an illiquid market, where the market maker's continuous trading incurs a stochastic linear price impact.…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation…
We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…
We investigate the well-posedness in the Hadamard sense and the absence of price manipulation in the optimal execution problem within the Almgren-Chriss framework, where the temporary and permanent impact parameters vary deterministically…
We solve the problem of super-hedging European or Asian options for discrete-time financial market models where executable prices are uncertain. The risky asset prices are not described by single-valued processes but measurable selections…
The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…
G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation…
In this paper, we consider mixed-integer nonsmooth constrained optimization problems whose objective/constraint functions are available only as the output of a black-box zeroth-order oracle (i.e., an oracle that does not provide derivative…