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To study the assumption that the utility maximization hypothesis implicitly adds to consumer theory, we consider a mathematical representation of pre-marginal revolution consumer theory based on subjective exchange ratios. We introduce two…
We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only…
In this paper, we consider three problems related to survival, growth, and goal reaching maximization of an investment portfolio with proportional net cash flow. We solve the problems in a market constrained due to borrowing prohibition. To…
Overconservatism has long been recognized as a major issue with robust optimization, despite its key advantages of tractability, performance guarantee, and limited information. To address this issue, a new criterion is proposed that can…
We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to…
We empirically test predictability on asset price by using stock selection rules based on maximum drawdown and its consecutive recovery. In various equity markets, monthly momentum- and weekly contrarian-style portfolios constructed from…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…
We study a discrete-time portfolio selection problem with partial information and maxi\-mum drawdown constraint. Drift uncertainty in the multidimensional framework is modeled by a prior probability distribution. In this Bayesian framework,…
During the Great Recession, Democrats in the United States argued that government spending could be utilized to "grease the wheels" of the economy in order to create wealth and to increase employment; Republicans, on the other hand,…
This paper studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…
As a firm varies the price of a product, consumers exhibit reference effects, making purchase decisions based not only on the prevailing price but also the product's price history. We consider the problem of learning such behavioral…
We consider a monopolistic seller in a market that may be segmented. The surplus of each consumer in a segment depends on the price that the seller optimally charges, which depends on the set of consumers in the segment. We study which…
In this paper, we consider a modified version of the control problem in a model free Markov decision process (MDP) setting with large state and action spaces. The control problem most commonly addressed in the contemporary literature is to…
A recent line of research has established a novel desideratum for designing approximately-revenue-optimal multi-item mechanisms, namely the buy-many constraint. Under this constraint, prices for different allocations made by the mechanism…
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.…
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…
Drawdowns measuring the decline in value from the historical running maxima over a given period of time, are considered as extremal events from the standpoint of risk management. To date, research on the topic has mainly focus on the side…
Constraint programming is used for a variety of real-world optimisation problems, such as planning, scheduling and resource allocation problems. At the same time, one continuously gathers vast amounts of data about these problems. Current…
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…