Constant Risk Aversion Coefficient Research Articles

Dynamic portfolio choice without cash

We consider the dynamic mean–variance portfolio choice without cash under a game theoretic framework. The mean–variance criterion is investigated in the situation where an investor allocates the wealth among risky assets while keeping no cash in a bank account. The problem is solved explicitly up to solutions of ordinary differential equations by applying the extended Hamilton–Jacobi–Bellman equation system. Given a constant risk aversion coefficient, the optimal allocation without a risk-free asset depends linearly on the current wealth, while that with a risk-free asset turns out to be independent of the current wealth. We also study the minimum-variance criterion, which can be viewed as an extension of the mean–variance model when the risk aversion coefficient tends to infinity. Calibration exercises demonstrate that for large investments, the mean–variance model without cash yields the highest certainty equivalent return for both short-term and long-term investments. Furthermore, the mean–variance portfolio choices with and without cash yield almost the same Sharpe ratio for an investment with large initial wealth.

Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model

In this paper, we study an optimal investment problem under the mean–variance criterion for defined contribution pension plans during the accumulation phase. To protect the rights of a plan member who dies before retirement, a clause on the return of premiums for the plan member is adopted. We assume that the manager of the pension plan is allowed to invest the premiums in a financial market, which consists of one risk-free asset and one risky asset whose price process is modeled by a jump–diffusion process. The precommitment strategy and the corresponding value function are obtained using the stochastic dynamic programming approach. Under the framework of game theory and the assumption that the manager’s risk aversion coefficient depends on the current wealth, the equilibrium strategy and the corresponding equilibrium value function are also derived. Our results show that with the same level of variance in the terminal wealth, the expected optimal terminal wealth under the precommitment strategy is greater than that under the equilibrium strategy with a constant risk aversion coefficient; the equilibrium strategy with a constant risk aversion coefficient is revealed to be different from that with a state-dependent risk aversion coefficient; and our results can also be degenerated to the results of He and Liang (2013b) and Björk et al. (2014). Finally, some numerical simulations are provided to illustrate our derived results.

Multi-portfolio time consistency for set-valued convex and coherent risk measures

Equivalent characterizations of multi-portfolio time consistency are deduced for closed convex and coherent set-valued risk measures on \(L^{p}({\varOmega,\mathcal{F},\mathbb{P}; \mathbb{R}^{d}})\) with image space in the power set of \(L^{p}({\varOmega,\mathcal{F}_{t},\mathbb{P}; \mathbb{R}^{d}})\). In the convex case, multi-portfolio time consistency is equivalent to a cocycle condition on the sum of minimal penalty functions. In the coherent case, multi-portfolio time consistency is equivalent to a generalized version of stability of the dual variables. As examples, the set-valued entropic risk measure with constant risk aversion coefficient is shown to satisfy the cocycle condition for its minimal penalty functions; the set of superhedging portfolios is shown to have in markets with proportional transaction costs the stability property and to satisfy in markets with convex transaction costs the composed cocycle condition; and a multi-portfolio time-consistent version of the set-valued average value at risk, the composed AV@R, is given, and its dual representation deduced.

Measuring Risk Aversion in a Name-Your-Own-Price Channel

This paper measures the risk aversion coefficients exhibited by online customers at a name-your-own-price (NYOP) intermediary that allowed the submission of subsequent offers. We present a decision analytic model to determine the optimal sequence of offers for a decision maker with a constant risk aversion coefficient. We show how the optimal sequence of offers can be determined by simple sensitivity analysis. We then discuss the inverse problem of estimating the risk aversion coefficient from a sequence of offers placed by a customer. We provide a direct expression for the risk aversion coefficient in terms of the increments between each two successive offers. This expression separates the estimation of the risk aversion from the remaining model parameters and enables its calculation directly by observing a sequence of offers from a customer. We then use field data from an NYOP firm to estimate the risk aversion that is exhibited throughout the online process. We find that customers exhibit relatively high risk aversion coefficients on Internet sites. Based on three different product groups, we also find that risk aversion is a significant variable in the offer strategy of the customers. To our knowledge, this is the first work that empirically examines risk aversion in a nonexperimental Internet-based NYOP setting.