The Optimal Conumption-investment Strategy With Loss Aversion Under Inflation Risk

With the accumulation of financial anomalies in the market and the development of the psychology,the classical financial theories centered around the hypothesis of‘rational man' has been challenged,and then ‘Behavioral Finance' which contains both economics and psychology emerges as the times require.The proposal of the‘Cumulative Prospect Theory'(CPT)by Kahneman and Tversky symbolized the behavioral economics mounted the stage of economics officially.The behavioral finance can well explain the anomalies in the financial market,and therefore more and more scholars added the element of behavioral finance to the models,especially the models of optimality.However,few of them combines both inflation risk and loss aversion.Inflation risk as a kind of background risk always exists in the investment,which indicates the necessity of taking inflation risk into account.The paper is aimed at finding the optimal consumption plan and the investment strategy among bonds,cash and the stock index for the agent with loss aversion who has the volitional characteristic of irrationality under inflation risk in a continuous model,and the market is complete.The paper uses the Vasicek model to describe the stochastic interest rate process and the expected inflation process,chooses the value function in ‘CPT' to describe the investor's preference of loss aversion,and then establishes the ‘S-' shaped real expected utility maximization model.The reference level can be fixed or changeable,the changeable reference level depends on the latest and the initial wealth(consumption)and is time-varying.Using the simple transformation to change the model with the originally stochastic reference level into an exogenous one,and the martingale methods and the replicating technique are applied to solve the optimal wealth and the optimal consumption-investment strategy.The paper does the numerical simulation to the explicit solutions to the model,the results show that both the optimal terminal wealth and the optimal consumption differs in good state and bad state,and decrease with the increase of the discounting factor(price kernel)in good state,and maintains fixed when in bad state.Also,the optimal investment proportions will decrease with the increase of the discounting factor,however,as the investor with loss aversion appears to be ‘risk-seeking' when he's in loss,he will continue investing in risky assets in order to retrieve loss when the market is in bad state,and the less risk-averse investor will be more risk-seeking.Additionally,the investor prefers bonds or cashes to the stock when the portfolio is a cash-bond-stock mixed one in order to avoid the inflation risk,and the optimal investment strategy is not affected by the expected inflation rate because the portfolio can hedge the inflation risk internally.