The identi cation of scenarios which have a particularly low or high P&L helps to get a better understanding of the portfolio's risk exposure. Therefore, the notions of safe (resp. dangerous) regions are introduced, which represent sets where the P&L is greater (resp. less) than a given critical level. In order to describe such sets in an easily interpretable way, one{dimensional intervals are ...

Abstract. The article is devoted to second order optimality in Markov decision processes. Attention is primarily focused on the reward variance for discounted models and undiscounted transient models (i.e. where the spectral radius of the transition probability matrix is less then unity). Considering the second order optimality criteria means that in the class of policies maximizing (or minimiz...

In this work, two models are proposed for electricity prices as energy commodity prices which in addition to mean-reverting properties have jumps and spikes, due to non-storability of electricity. The models are simulated using an Euler scheme, and then the Monte-Carlo method is used to estimate the expectation of the discounted cash-flow under historical probability, which is considered as the...

In this paper we first consider the expectation of the total discounted claim costs up to the time of ruin, and then, more generally, we study the expectation of the total discounted operating costs up to the time of default, which is the first passage time of a surplus process downcrossing a given level. These two quantities include the expected discounted penalty function at ruin or the Gerbe...

The discounted utilitarian criterion for infinite horizon social choice has been criticized for treating generations unequally. We propose an extended rank-discounted utilitarian (ERDU) criterion instead. The criterion amounts to discounted utilitarianism on non-decreasing streams, but it treats all generations impartially: discounting becomes the mere expression of intergenerational inequality...

Hierarchical reinforcement learning (RL) is a general framework which studies how to exploit the structure of actions and tasks to accelerate policy learning in large domains. Prior work in hierarchical RL, such as the MAXQ method, has been limited to the discrete-time discounted reward semiMarkov decision process (SMDP) model. This paper generalizes the MAXQ method to continuous-time discounte...

This paper studies the exposure of the stock prices of Australian gold-mining firms to changes in gold prices and the valuation effects of gold price exposure. Goldmining firms have significant gold price exposure; the price of the average goldmining stock moves 0.76% for each 1.00% change in Australian-dollar-denominated gold prices. Evidence from the behaviour of stock price sensitivities sug...

We present a decision theoretic framework in which agents are learning about market behavior and that provides microfoundations for models of adaptive learning. Agents are ‘internally rational’, i.e., maximize discounted expected utility under uncertainty given consistent subjective beliefs about the future, but agents may not be ‘externally rational’, i.e., may not know the true stochastic pro...