A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge weights, which values a run by the discounted sum of visited edge weights. More precisely, the weight in the i-th position of the run is divided by λ, where the discount factor λ is a fixed rational number greater than 1. Discounted summation is a common and useful measuring scheme, especially for infinite sequenc...

We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears to be rational but cannot be represented with any discounted expected utility. A straightforward modification to discounted expected utility leads to inconsis...

This lemma allows us to find a minimax estimator for a particular tractable submodel, and then show that the worst-case risk for the full model is equal to that of the submodel (that is, the worst-case risk doesn’t rise as you go to the full model). In this case, using the Lemma, we can argue that the estimator we found is also minimax for the full model. This was similar to how we justified mi...

We consider a price-setting newsvendor problem with partial information. The newsvendor does not know the price-dependent probability distribution of demand, but is able to estimate lower and upper limits of the market size and consumer willingness-to-pay. The objective is to minimize the maximum loss in expected profit, or minimax regret. We derive closed-form expressions for optimal quantity ...

This research examines the impact of forest management regimes, with various degrees of restriction, on forest conservation in a dry deciduous Indian forest landscape. Forest change is mapped using Landsat satellite images from 1977, 1990, 1999, and 2011. The landscape studied has lost 1478 km2 of dense forest cover between 1977 and 2011, with a maximum loss of 1002 km2 of dense forest between ...

This paper deals with constrained optimization of Markov Decision Processes with a countable state space, compact action sets, continuous transition probabilities, and upper semi-continuous reward functions. The objective is to maximize the expected total discounted reward for one reward function, under several inequality constraints on similar criteria with other reward functions. Suppose a fe...

We show that several basic discounted properties of probabilistic pushdown automata related both to terminating and non-terminating runs can be efficiently approximated up to an arbitrarily small given precision.

We construct arbitrage strategies for a financial market that consists of a money market account and a stock whose discounted price follows a fractional Brownian motion with drift or an exponential fractional Brownian motion with drift. Then we show how arbitrage can be excluded from these models by restricting the class of trading strategies.