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Although maximizing median and quantiles is intuitively appealing and has an axiomatic foundation, it is difficult to study the optimal portfolio strategy due to the discontinuity and time inconsistency in the objective function. We use 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.…
We consider the optimal dividend problem under a habit formation constraint that prevents the dividend rate to fall below a certain proportion of its historical maximum, the so-called drawdown constraint. This is an extension of the optimal…
This paper studies the properties of the optimal portfolio-consumption strategies in a {finite horizon} robust utility maximization framework with different borrowing and lending rates. In particular, we allow for constraints on both…
The "standard" Merton formulation of optimal investment and consumption involves optimizing the integrated lifetime utility of consumption, suitably discounted, together with the discounted future bequest. In this formulation the utility of…
We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real…
We study optimal investment problems under the framework of cumulative prospect theory (CPT). A CPT investor makes investment decisions in a single-period financial market with transaction costs. The objective is to seek the optimal…
This paper investigates the consumption and risk taking decision of an economic agent with partial irreversibility of consumption decision by formalizing the theory proposed by Duesenberry (1949). The optimal policies exhibit a type of the…
We consider a diffusion risk model where dividends are paid at rate $U(t) \in [0, u_0]$. We are interested in maximising the dividend payments under a drawdown constraint, that is, we penalise a drawdown size larger than a level $d > 0$. We…
It is widely recognized that when classical optimal strategies are applied with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the…
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…
The optimal strategies for a long-term static investor are studied. Given a portfolio of a stock and a bond, we derive the optimal allocation of the capitols to maximize the expected long-term growth rate of a utility function of the…
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA…
We study optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values…
We consider the optimal investment problem for Black-Scholes type financial market with bounded VaR measure on the whole investment interval $[0,T]$. The explicit form for the optimal strategies is found.
We are witnessing an increasing use of data-driven predictive models to inform decisions. As decisions have implications for individuals and society, there is increasing pressure on decision makers to be transparent about their decision…
This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption…
We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization…
In natural perception, different items (objects) in a scene are rarely equally relevant to the observer. The brain improves performance by directing attention to the most relevant items, for example the ones most likely to be probed. For a…
Decision-changing imitation is a prevalent phenomenon in financial markets, where investors imitate others' decision-changing rates when making their own investment decisions. In this work, we study the optimal investment problem under the…