On the total reward variance for continuous-time Markov reward chains

Dijk, N.M. van; Sladký, Karel

doi:10.1239/jap/1165505206

Cited by 7 publications

(1 citation statement)

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“…Sladky and van Dijk [45], [46] have given results for discrete- and continuous-time chains with fixed rewards. Benito [42] provides variances for discrete chains with random rewards; my proof of Proposition 1 follows his approach.…”

Section: Discussionmentioning

confidence: 99%

Beyond R0: Demographic Models for Variability of Lifetime Reproductive Output

Caswell

2011

PLoS ONE

156

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The net reproductive rate measures the expected lifetime reproductive output of an individual, and plays an important role in demography, ecology, evolution, and epidemiology. Well-established methods exist to calculate it from age- or stage-classified demographic data. As an expectation, provides no information on variability; empirical measurements of lifetime reproduction universally show high levels of variability, and often positive skewness among individuals. This is often interpreted as evidence of heterogeneity, and thus of an opportunity for natural selection. However, variability provides evidence of heterogeneity only if it exceeds the level of variability to be expected in a cohort of identical individuals all experiencing the same vital rates. Such comparisons require a way to calculate the statistics of lifetime reproduction from demographic data. Here, a new approach is presented, using the theory of Markov chains with rewards, obtaining all the moments of the distribution of lifetime reproduction. The approach applies to age- or stage-classified models, to constant, periodic, or stochastic environments, and to any kind of reproductive schedule. As examples, I analyze data from six empirical studies, of a variety of animal and plant taxa (nematodes, polychaetes, humans, and several species of perennial plants).

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Section: Discussionmentioning

confidence: 99%

Beyond R0: Demographic Models for Variability of Lifetime Reproductive Output

Caswell

2011

PLoS ONE

156

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On minimizing downside risk in make‐to‐stock, risk‐averse firms

Arreola‐Risa

2020

Naval Research Logistics

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Consider a single‐product, make‐to‐stock, risk‐averse firm with stochastic demand and manufacturing capacity. Temporarily unfilled demands are back‐ordered. Total cost is equal to the sum of inventory‐holding and back‐ordering costs over a continuous‐time, finite planning horizon. In this article, we study the problem of finding the base‐stock level that minimizes total cost conditional value‐at‐risk (CVaR), or total cost CVaR for short. We demonstrate that total cost CVaR is both convex in the base‐stock level and increasing in risk aversion. We derive a closed‐form approximation of total cost which is asymptotically exact in the planning horizon length. The approximation leads to a relatively simple determination of optimal base‐stock levels which are reasonably accurate for practical applications. We make observations and identify findings regarding the impact on optimal base‐stock levels of changes in risk aversion, manufacturing capacity, inventory‐holding and back‐ordering costs, and planning horizon length. We provide a detailed description of how our research results were applied in a real‐world, supply‐chain design project.

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Mean-Variance Problems for Finite Horizon Semi-Markov Decision Processes

Huang

Guo

2014

Appl Math Optim

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On the total reward variance for continuous-time Markov reward chains

Cited by 7 publications

References 20 publications

Beyond R0: Demographic Models for Variability of Lifetime Reproductive Output

Beyond R0: Demographic Models for Variability of Lifetime Reproductive Output

On minimizing downside risk in make‐to‐stock, risk‐averse firms

Mean-Variance Problems for Finite Horizon Semi-Markov Decision Processes

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