Related papers: Minimizing the Probability of Lifetime Drawdown un…
The consumption function maps current wealth and the exogenous state to current consumption. We prove the existence and uniqueness of a consumption function when the agent has a preference for wealth. When the period utility functions are…
We consider a stochastic model of investment on an asset of a stock market for a prudent investor. She decides to buy permanent goods with a fraction $\a$ of the maximum amount of money owned in her life in order that her economic level…
We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a reversible life annuity. The surrender charge of a life annuity is a proportion of its…
We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk free asset and in a risky asset, governed by the Black-Scholes equation. There is a…
In life-cycle economics the Samuelson paradigm (Samuelson, 1969) states that the optimal investment is in constant proportions out of lifetime wealth composed of current savings and the present value of future income. It is well known that…
This paper considers an optimal life insurance for a householder subject to mortality risk. The household receives a wage income continuously, which is terminated by unexpected (premature) loss of earning power or (planned and intended)…
Empirical evidence shows that wealthy households have substantially higher saving rates and markedly lower marginal propensity to consume (MPC) than other groups. Existing theory cannot account for this pattern unless under restrictive…
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose…
We propose martingale consumption as a natural, desirable consumption pattern for any given (proportional) investment strategy. The idea is to always adjust current consumption so as to achieve level expected future consumption under the…
In this paper, we study a stochastic optimal control problem with stochastic volatility. We prove the sufficient and necessary maximum principle for the proposed problem. Then we apply the results to solve an investment, consumption and…
We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor's capital. We determine the optimal fraction of…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a…
Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order to study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At…
In this article we consider a special case of an optimal consumption/optimal portfolio problem first studied by Constantinides and Magill and by Davis and Norman, in which an agent with constant relative risk aversion seeks to maximise…
In this paper,we study the individual's optimal retirement time and optimal consumption under habitual persistence. Because the individual feels equally satisfied with a lower habitual level and is more reluctant to change the habitual…
We consider the problem of optimal investment with random endowment in a Black--Scholes market for an agent with constant relative risk aversion. Using duality arguments, we derive an explicit expression for the optimal trading strategy,…
This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework. A key aspect of our study involves the agent's option to choose…
We study an optimal investment and consumption problem over a finite-time horizon, in which an individual invests in a risk-free asset and a risky asset, and evaluate utility using a general utility function that exhibits loss aversion with…
We study the optimal investment problem for a homogeneous collective of $n$ individuals investing in a Black-Scholes model subject to longevity risk with Epstein--Zin preferences. %and with preferences given by power utility. We compute…
This paper studies an optimal consumption-investment problem for an investor whose instantaneous utility depends on both consumption and wealth, and the investor faces a general borrowing constraint that the investment amount in the risky…