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Shortfall aversion reflects the higher utility loss of spending cuts from a reference than the utility gain from similar spending increases. Inspired by Prospect Theory's loss aversion and the peak‐end rule, this paper posits a model of utility from spending scaled by past peak spending. In contrast to traditional models, which call for spending rates proportional to wealth, the optimal policy in this model implies a constant spending rate equal to the historical peak when wealth is relatively large. The spending rate increases when wealth reaches a model‐determined multiple of peak spending. In 1926–2015, shortfall‐averse spending is smooth and typically increasing.

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This paper focuses on optimal asset allocation with stochastic interest rates in regime-switching models. A class of stochastic optimal control problems with Markovian regime-switching is formulated for which a verification theorem is provided. The theory is applied to solve two portfolio optimization problems (a portfolio of stock and savings account and a portfolio of mixed stock, bond and savings account) while a regime-switching Vasicek model is assumed for the interest rate. Closed-form solutions are obtained for a regime-switching power utility function. Numerical results are provided to illustrate the impact of regime-switching on the optimal investment decisions.

A continuous-time and infinite-horizon optimal investment and consumption model with proportional transaction costs and regime-switching was considered in Liu [4]. A power utility function was specifically studied in [4]. This paper considers the case of log utility. Using a combination of viscosity solution to the Hamilton-Jacobi-Bellman (HJB) equation and convex analysis of the value function, we are able to derive the characterizations of the buy, sell and no-transaction regions that are regime-dependent. The results generalize Shreve and Soner [6] that deals with the same problem but without regime-switching.