Uncertainty, Jump Risk, And The Mystery Of Sound Investment Decisions And Equity Premiu

At present,the world is undergoing profound changes.The sources of global turbulence and risk points have increased significantly.The world economy is also facing various uncertainties.A steady stream of internal and external shocks.The internal and external environment facing my country’s economy is more complex and severe.TRare events such as the 1997 Southeast Asian financial crisis,the September 11 terrorist attacks,the 2008 financial crisis,the European debt crisis,Brexit,and COVID-19 raging around the world,may have a huge impact on the financial market at all times.These events are often unpredictable,and it is difficult to accurately predict how long they will last,but their influence is huge to economic development and they will cause a jump in financial market earnings.At the same time,this uncertain environment will be a challenge for estimating an accurate optimal estimation model,so adding model ambiguity and using a robust model to make decisions has become the best choice for many decision makers.Therefore,this paper selects model uncertainty,jump risk,and the time-varying rare disaster models what describes these events and adds model uncertainty to the jump risk,aiming to help decision makers overcome model misspecification problem and provide a robust model which is used as a reference basis for decision-making.First,this paper studies how hedge fund managers make the optimal robust investment decisions with ambiguity.Based on the classic hedge fund high-water-mark contract model,this paper adds lock-wealth and considers the ambiguity belief of the hedge fund manager in the return process of risky asset,thereby studying the robust fund leverage choice and private investment decision.This paper uses the stochastic control method to solve the Hamilton-Jacobi-Bellman-Isaacs(HJBI)equation and martingale pricing method to obtain a solution for the optimal robust leverage.Through numerical analysis and comparative static analysis,it is found that ambiguity has a U-shaped effect on the optimal fund leverage since the manager trade off risk and return between fund investment and private investment.That is the optimal fuud leverage is monotonically decreasing with ambiguity when the uncertainty is relatively small,but while ambiguity exceeds a certain value,the optimal fuud leverage increases monotonically with ambiguity.Moreover,this result is robust and have passed the proof of comparative static analysis under a mild regularity condition.Secondly,this paper studies how ambiguity and jump risk affect optimal robust portfolio and consumption choice when the investor faces with the sustainable consumption constraint and undiminished expected utility constraint.The study found that jump risk and ambiguity have different effects on portfolio and consumption choice.Under the sustainable consumption constraint,the impact of ambiguity on risk-taking is a two-way effect,derisk and gambling with different risk-free rates.The impact of jump amplitude on risk-taking is an inverted U shape since the constraint the intertemporal consumption smoothing and wealth accumulation and show a skew effect since risk-taking is more sensitive to negative news than to good news.Under the undiminished expected utility constraint,the risk-taking is the same as the unconstrained situation,the ambiguity reduces the risk-taking,and the impact of the jump amplitude on the risk-taking is monotonously increasing.The onstraint makes the investor precautiously save.Precautionary savings increase in ambiguity,but monotonously decrease in the jump amplitude.The two constraints make consumption not be chosen and deviate from the optimal value,resulting in welfare loss.Welfare loss is determined by the deviation between constrained consumption and unconstrained consumption.Finally,this paper studies the rare disaster model and the equity premium puzzle.In order to increase the interpretation of the rare disaster model to the equity premium puzzle,this paper introduce ambiguity to the endowment process and the intensity and magnitude of jump risk in the rare disaster model.The expression of the equity premium is obtained by solving the HBJI equation and the martingale pricing method,and decomposed a separate impact of ambiguity.Through numerical analysis,it is found that the new model can explain the equity premium puzzle.The addition of ambiguity increases the interpretation of equity premium in the model.This conclusion is still valid even if a parial default on government securities defaults is considered.