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We study hedging and pricing of unattainable contingent claims in anon-Markovian regime-switching financial model. Our financial market consistsof a bank account and a risky asset whose dynamics are driven by a Brownianmotion and a multivariate counting process with stochastic intensities. Theinterest rate, drift, volatility and intensities fluctuate over time and, inparticular, they depend on the state (regime) of the economy which is modelledby the multivariate counting process. Hence, we can allow for stressed marketconditions. We assume that the trajectory of the risky asset is continuousbetween the transition times for the states of the economy and that the valueof the risky asset jumps at the time of the transition. We find the hedgingstrategy which minimizes the instantaneous mean-variance risk of the hedger'ssurplus and we set the price so that the instantaneous Sharpe ratio of thehedger's surplus equals a predefined target. We use Backward StochasticDifferential Equations. Interestingly, the instantaneous mean-variance hedgingand instantaneous Sharpe ratio pricing can be related to no-good-deal pricingand robust pricing and hedging under model ambiguity. We discuss key propertiesof the optimal price and the optimal hedging strategy. We also use our resultsto price and hedge mortality-contingent claims with financial components(equity-linked insurance claims) in a combined insurance and regime-switchingfinancial model.

Instantaneous mean-variance hedging and instantaneous Sharpe ratio  pricing in a regime-switching financial model, with applications to  equity-linked claims