Related papers: Optimal Annuitization Time under a Mortality Shock
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…
We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of…
This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be…
Motivated by the AIG bailout case in the financial crisis of 2007-2008, we consider an insurer who wants to maximize the expected utility of the terminal wealth by selecting optimal investment and risk control strategies. The insurer's risk…
In this paper, we develop a deep neural network approach to solve a lifetime expected mortality-weighted utility-based model for optimal consumption in the decumulation phase of a defined contribution pension system. We formulate this…
This paper addresses the risk-minimization problem, with and without mortality securitization, \`a la F\"ollmer-Sondermann for a large class of equity-linked mortality contracts when no model for the death time is specified. This framework…
We consider an expected utility maximization problem where the utility function is not necessarily concave and the time horizon is uncertain. We establish a necessary and sufficient condition for the optimality for general non-concave…
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on…
This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function.…
We investigate models of the life annuity insurance when the company invests its reserve into a risky asset with price following a geometric Brownian motion. Our main result is an exact asymptotic of the ruin probabilities for the case of…
We analyze an irreversible investment decision for a project which yields a flow of future operating profits given by a geometric Brownian motion with unknown drift. In contrast to similar optimal stopping problems with incomplete…
In this paper we consider a company whose assets and liabilities evolve according to a correlated bivariate geometric Brownian motion, such as in Gerber and Shiu (2003). We determine what dividend strategy maximises the expected present…
Given two probability measures $\mu, \nu$ on $\mathbb{R}^d$, in subharmonic order, we describe optimal stopping times $\tau$ that maximize/minimize the cost functional $\mathbb{E} |B_0 - B_\tau|^{\alpha}$, $\alpha > 0$, where $(B_t)_t$ is…
We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset…
This paper proposes a paradigm shift in the valuation of long term annuities, away from classical no-arbitrage valuation towards valuation under the real world probability measure. Furthermore, we apply this valuation method to two examples…
In this work, we address the optimal retirement problem in the presence of a stochastic wage, formulated as a free boundary problem. Specifically, we explore an incomplete market setting where the wage cannot be perfectly hedged through…
We investigate optimal stopping problems for systems driven by the Brownian sheet. Our analysis is divided into two parts. In the first part we derive explicit solutions to two optimal stopping problems for the exponentially discounted…
In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal…
We find the optimal indemnity to minimize the probability of ruin when premium is calculated according to the distortion premium principle with a proportional risk load, and admissible indemnities are such that both the indemnity and…
We consider a discrete-time version of the popular optimal dividend pay-out problem in risk theory. The novel aspect of our approach is that we allow for a risk averse insurer, i.e., instead of maximising the expected discounted dividends…