Related papers: Optimal investment under partial information and r…
We study the Merton problem of optimal consumption-investment for the case of two investors sharing a final wealth. The typical example would be a husband and wife sharing a portfolio looking to optimize the expected utility of consumption…
We study the regulation of a monopolistic firm using a robust-design approach. We solve for the policy that minimizes the regulator's worst-case regret, where the regret is the difference between his complete-information payoff minus his…
We consider an optimal investment and risk control problem for an insurer under the mean-variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate an alternative time-consistent problem…
This paper considers nonlinear regular-singular stochastic optimal control of large insurance company. The company controls the reinsurance rate and dividend payout process to maximize the expected present value of the dividend pay-outs…
Consider a multi-agent network comprised of risk averse social sensors and a controller that jointly seek to estimate an unknown state of nature, given noisy measurements. The network of social sensors perform Bayesian social learning -…
We consider a problem of optimal investment with intermediate consumption and random endowment in an incomplete semimartingale model of a financial market. We establish the key assertions of the utility maximization theory assuming that…
When selling information products, the seller can provide some free partial information to change people's valuations so that the overall revenue can possibly be increased. We study the general problem of advertising information products by…
Several well-established benchmark predictors exist for Value-at-Risk (VaR), a major instrument for financial risk management. Hybrid methods combining AR-GARCH filtering with skewed-$t$ residuals and the extreme value theory-based approach…
Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff. Economic intuition suggests that…
We study a robust utility maximization problem in the case of an incomplete market and logarithmic utility with general stochastic constraints, not necessarily convex. Our problem is equivalent to maximizing of nonlinear expected…
We study a class of stochastic optimal design problems for elliptic partial differential equations in divergence form, where the coefficients represent mixtures of two conducting materials. The objective is to minimize a generalized risk…
The robust option pricing problem is to find upper and lower bounds on fair prices of financial claims using only the most minimal assumptions. It contrasts with the classical, model-based approach and gained prominence in the wake of the…
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.…
Optimal portfolio allocation is often formulated as a constrained risk problem, where one aims to minimize a risk measure subject to some performance constraints. This paper presents new Bayesian Optimization algorithms for such constrained…
The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a…
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition…
A monopoly platform sells either a risky product (with unknown utility) or a safe product (with known utility) to agents who sequentially arrive and learn the utility of the risky product by the reporting of previous agents. It is costly…
This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our…
We give explicit solutions for utility maximization of terminal wealth problem $u(X_T)$ in the presence of Knightian uncertainty in continuous time $[0,T]$ in a complete market. We assume there is uncertainty on both drift and volatility of…
Minimizing volatility and adjustment costs is of central importance in many economic environments, yet it is often complicated by evolving feasibility constraints. We study a decision maker who repeatedly selects an action from a…