Related papers: Dealing with the Inventory Risk. A solution to the…
Stochastic production planning problems were studied in several works; the model with one production good was discussed in [3]. The extension to several economic goods is not a trivial issue as one can see from the recent works [4], [5] and…
We present a new microscopic stochastic model for an ensemble of interacting investors that buy and sell stocks in discrete time steps via limit orders based on individual forecasts about the price of the stock. These orders determine the…
We use a white noise approach to study the problem of optimal inside control of a stochastic delay equation driven by a Brownian motion B and a Poisson random measure N. In particular, we use Hida-Malliavin calculus and the Donsker delta…
In this paper, we assume an insure is allowed to purchase proportional reinsurance and can invest his or her wealth into the financial market where a savings account, stocks and bonds are available. Different from classical optimal…
We study a single risky financial asset model subject to price impact and transaction cost over an finite time horizon. An investor needs to execute a long position in the asset affecting the price of the asset and possibly incurring in…
Time-consistency is an essential requirement in risk sensitive optimal control problems to make rational decisions. An optimization problem is time consistent if its solution policy does not depend on the time sequence of solving the…
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…
We develop a Euclidean path-integral control to characterize optimal firm behavior in an economy governed by Walrasian equilibrium, Pareto efficiency, and non-cooperative Markovian feedback Nash equilibrium. The approach recasts the problem…
We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of…
In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random…
Optimized certainty equivalents (OCEs) is a family of risk measures widely used by both practitioners and academics. This is mostly due to its tractability and the fact that it encompasses important examples, including entropic risk…
This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss, or only on the liquidity-consuming orders like Obizhaeva and Wang,…
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…
This paper considers the problem faced by a bank which trades in the funds market so as to maintain the reserve requirements and minimize the costs of doing that. We work in a stochastic paradigm and the reserve requirements are determined…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
We consider the issue of a market maker acting at the same time in the lit and dark pools of an exchange. The exchange wishes to establish a suitable make-take fees policy to attract transactions on its venues. We first solve the stochastic…
We consider an illiquid financial market with different regimes modeled by a continuous-time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the…
We consider the problem of supply and demand balancing that is stated as a minimization problem for the total expected revenue function describing the behavior of both consumers and suppliers. In the considered market model we assume that…
We consider the mean--variance portfolio optimization problem under the game theoretic framework and without risk-free assets. The problem is solved semi-explicitly by applying the extended Hamilton--Jacobi--Bellman equation. Although the…
In this paper, we study the following nonlinear backward stochastic integral partial differential equation with jumps \begin{equation*} \left\{ \begin{split} -d V(t,x) =&\displaystyle\inf_{u\in U}\bigg\{H(t,x,u, DV(t,x),D \Phi(t,x), D^2…