Dual Bounds for Periodical Stochastic Programs

A construction of the dual of a periodical formulation of infinite-horizon linear stochastic programs with a discount factor is discussed. The dual problem is used for computing a deterministic upper bound for the optimal value of the considered multistage stochastic program. Numerical experiments demonstrate behavior of that upper bound, especially when the discount factor is close to one.

Durable Goods Adoption and the Consumer Discount Factor: A Case Study of the Norwegian Book Market

We exploit a change in Norway’s fixed book pricing policies to construct exclusion restrictions with which to identify consumers’ discount factor. We assume that the policy change generated an unanticipated, exogenous shock to consumers’ expectations about future price cuts. Our findings suggest that consumers are much more impatient than would be implied by the real rate of interest, challenging the standard assumed rate of discounting in the extant literature on dynamic demand estimation. The high rate of consumer impatience is consistent with laboratory studies in the behavioral economics and decision-making literatures. This paper was accepted by Matthew Shum, marketing.

The Stackelberg Games of Water Extraction with Myopic Agents

We consider a discrete-time, infinite-horizon dynamic game of groundwater extraction. A Water Agency charges an extraction cost to water users and controls the marginal extraction cost so that it depends not only on the level of groundwater but also on total water extraction (through a parameter [Formula: see text] that represents the degree of strategic interactions between water users) and on rainfall (through parameter [Formula: see text]). The water users are selfish and myopic, and the goal of the agency is to give them incentives so as to improve their total discounted welfare. We look at this problem in several situations. In the first situation, the parameters [Formula: see text] and [Formula: see text] are considered to be fixed over time. The first result shows that when the Water Agency is patient (the discount factor tends to 1), the optimal marginal extraction cost asks for strategic interactions between agents. The contrary holds for a discount factor near 0. In a second situation, we look at the dynamic Stackelberg game where the Agency decides at each time what cost parameter they must announce. We study theoretically and numerically the solution to this problem. Simulations illustrate the possibility that threshold policies are good candidates for optimal policies.

Designing Annuities with Flexibility Opportunities in an Uncertain Mortality Scenario

We consider annuity designs in which the benefit amount is allowed to fluctuate (up or down), based on a given mortality/longevity experience. This way, guarantees are relaxed in respect of traditional annuity arrangements. On the other hand, while the annuitant is exposed to the risk of a future reduction of the benefit amount because of higher longevity, he/she can immediately take advantage of a lower premium loading, as well as of a future increase of the benefit amount in the case of higher mortality. Flexibility in the annuity design could be welcomed by individuals, as the conservative features of traditional products partly explain their lack of attractiveness in most markets. To further contribute to the flexibility of the product, we suggest a pricing structure based on periodic fees applied to the policy fund, instead of the usual upfront loading at issue. Periodic fees are more suitable to support a revision of the arrangement after issue, which is currently not allowed in traditional annuity products. We show that periodic fees can be introduced by identifying a discount factor to be used for pricing and reserving. We assume stochastic mortality, and we compare alternative mortality/longevity linking solutions, by assessing the periodic fees and other quantities.

Stochastic maximum power point tracking of photovoltaic energy system under partial shading conditions

A large portion of the available power generation of a photovoltaic (PV) array could be wasted due to partial shading, temperature and irradiance effects, which create current/voltage imbalance between the PV modules. Partial shading is a phenomenon which occurs when some modules in a PV array receive non-uniform irradiation due to dust, cloudy weather or shadows of nearby objects such as buildings, trees, mountains, birds etc. Maximum power point tracking (MPPT) techniques are designed in order to deal with this problem. In this research, a Markov Decision Process (MDP) based MPPT technique is proposed. MDP consists of a set of states, a set of actions in each state, state transition probabilities, reward function, and the discount factor. The PV system in terms of the MDP framework is modelled first and once the states, actions, transition probabilities, and reward function, and the discount factor are defined, the resulting MDP is solved for the optimal policy using stochastic dynamic programming. The behavior of the resulting optimal policy is analyzed and characterized, and the results are compared to existing MPPT control methods.

The Use of Trapezoidal Oriented Fuzzy Numbers in Portfolio Analysis

Oriented fuzzy numbers are a convenient tool to manage an investment portfolio as they enable the inclusion of uncertain and imprecise information about the financial market in a portfolio analysis. This kind of portfolio analysis is based on the discount factor. Thanks to this fact, this analysis is simpler than a portfolio analysis based on the return rate. The present value is imprecise due to the fact that it is modelled with the use of oriented fuzzy numbers. In such a case, the expected discount factor is also an oriented fuzzy number. The main objective of this paper is to conduct a portfolio analysis consisting of the instruments with the present value estimated as a trapezoidal oriented fuzzy number. We consider the portfolio elements as being positively and negatively oriented. We test their discount factor. Due to the fact that adding oriented fuzzy numbers is not associative, a weighted sum of positively oriented discount factors and a weighted sum of negatively oriented factors is calculated and consequently a portfolio discount factor is obtained as a weighted addition of both sums. Also, the imprecision risk of the obtained investment portfolio is estimated using measures of energy and entropy. All theoretical considerations are illustrated by an empirical case study.