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We consider the problem of maximizing expected utility from terminal wealth in models with stochastic factors. Using martingale methods and a conditioning argument, we determine the optimal strategy for power utility under the assumption…

A dynamic model of collective consumption and saving decisions made by a finite number of agents with constant but different discount rates is developed. Collective utility is a weighted sum of individual utilities with time-varying utility…

Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…

We study risk-aware linear policy approximations for the optimal operation of an energy system with stochastic wind power, storage, and limited fuel. The resulting problem is a sequential decision-making problem with rolling forecasts. In…

Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study the optimal dividends strategy in dual…

We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…

This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable,…

In economic studies and popular media, interest rates are routinely cited as a major factor behind commodity price fluctuations. At the same time, the transmission channels are far from transparent, leading to long-running debates on the…

We provide a new foundation of risk aversion by showing that this attitude is fully captured by the propensity to seize insurance opportunities. Our foundation, which applies to all probabilistically sophisticated preferences, well accords…

The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite sets…

We determine forest lease value and optimal harvesting strategies under model parameter uncertainty within stochastic bio-economic models that account for catastrophe risk. Catastrophic events are modeled as a Poisson point process, with a…

Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds…

A central result in statistical theory is Pinsker's theorem, which characterizes the minimax rate in the normal means model of nonparametric estimation. In this paper, we present an extension to Pinsker's theorem where estimation is carried…

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)…

We use the stochastic approach to investigate the measure for slow roll eternal inflation. The probability for the universe of a given Hubble radius can be calculated in this framework. In a solvable model, it is shown that the probability…

We study an asset allocation stochastic problem with restriction for a defined-contribution pension plan during the accumulation phase. We consider a financial market with stochastic interest rate, composed of a risk-free asset, a real zero…

We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following geometric Brownian motion as in the Black-Scholes model. Under a constant rate of consumption, we find the…

This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…

We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of…

This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…