Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system

This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. The representation of the cost functional for the stochastic LQ optimal control problem of Markovian regime switching system is derived by the technique of It{\^o}'s formula with jumps. For the stochastic LQ optimal control problem of Markovian regime switching system, we establish the equivalence between the open-loop (closed-loop, resp.) solvability and the existence of an adapted solution to the corresponding forward-backward stochastic differential equation with constraint (the existence of a regular solution to Riccati equations). Also, we analyze the interrelationship between the strongly regular solvability of Riccati equations and the uniform convexity of the cost functional. Finally, we present an example which is open-loop solvable but not closed-loop solvable.

A multi-period risk sharing supply chain contract under consideration of price and demand uncertainties

Exchange rate is extremely volatile and displays a Markovian regime switching property. This report proposes a multi-period procurement problem with a flexible quantity risk-sharing supply contract that may provide a prevention against exchange rate (FX) fluctuations for international traders. The buyer assumed to be encountered with a random price modelled by a regime-switching geometric Brownian motion and also random demand. The proposed risk sharing supply contract model helps to compensate supplier for the depreciating market price and also helps buyer when purchase price increases. According to the author’s knowledge, none of the studies in the literature considers a risk-sharing supply contract with random demand and random price while modelling the exchange rates by regime switching approach. Multi-period lattice model is developed for valuation of risk-sharing supply contract. The problem is solved with using dynamic programming approach. A numerical example and sensitivity analyses are presented to illustrate the proposed model.

A multi-period risk sharing supply chain contract under consideration of price and demand uncertainties

Exchange rate is extremely volatile and displays a Markovian regime switching property. This report proposes a multi-period procurement problem with a flexible quantity risk-sharing supply contract that may provide a prevention against exchange rate (FX) fluctuations for international traders. The buyer assumed to be encountered with a random price modelled by a regime-switching geometric Brownian motion and also random demand. The proposed risk sharing supply contract model helps to compensate supplier for the depreciating market price and also helps buyer when purchase price increases. According to the author’s knowledge, none of the studies in the literature considers a risk-sharing supply contract with random demand and random price while modelling the exchange rates by regime switching approach. Multi-period lattice model is developed for valuation of risk-sharing supply contract. The problem is solved with using dynamic programming approach. A numerical example and sensitivity analyses are presented to illustrate the proposed model.

Estimation of Uncertainty in Mortality Projections Using State-Space Lee-Carter Model

The study develops alternatives of the classical Lee-Carter stochastic mortality model in assessment of uncertainty of mortality rates forecasts. We use the Lee-Carter model expressed as linear Gaussian state-space model or state-space model with Markovian regime-switching to derive coherent estimates of parameters and to introduce additional flexibility required to capture change in trend and non-Gaussian volatility of mortality improvements. For model-fitting, we use a Bayesian Gibbs sampler. We illustrate the application of the models by deriving the confidence intervals of mortality projections using Lithuanian and Swedish data. The results show that state-space model with Markovian regime-switching adequately captures the effect of pandemic, which is present in the Swedish data. However, it is less suitable to model less sharp but more prolonged fluctuations of mortality trends in Lithuania.