Comonotonic Approximations for Optimal Portfolio Selection Problems

By Jan Dhaene, Steven Vanduffel, Marc J. Goovaerts, Rob Kaas, David Vyncke. 2005

92 citations recorded by the source corpus.

We investigate multiperiod portfolio selection problems in a Black & Scholes type market where a basket of 1 riskfree and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of ’constant mix’ portfolios. First, we consider the portfolio selection problem of a decision maker who invests money at predetermined points in time in order to obtain a target capital at the end of the time period under consideration. A second problem concerns a decision maker who invests some amount of money (the initial wealth or provision) in order to be able to fullfil a series of future consumptions or payment obligations. Several optimality criteria and their interpretation within Yaari’s dual theory of choice under risk are presented. For both selection problems, we propose accurate approximations based on the concept of comonotonicity, as studied in Dhaene, Denuit, Goovaerts, Kaas & Vyncke (2002 a,b). Our analytical approach avoids simulation, and hence reduces the computing effort drastically.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/221cf41989c4f82aa7f97e320d47ebf1270c2390

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

In Management Science and Operations Research

Citations in the corpus

Comparing Approximations for Risk Measures of Sums of Nonindependent Lognormal Random Variables (2005, unknown): “Also notice that the comonotonic approximations that we presented here can easily be transformed to the case when accumulating saving amounts to a final value, as well as to the case where the cash flow payments vary from period to period; see Dhaene et al. (2005).”
Value-at-Risk Bounds with Variance Constraints (2015, unknown): “For applications of this idea in various contexts, such as the modeling of annuities, option pricing and portfolio selection problems, see Curran (1994), Darkiewicz et al. (2009), Vanduffel et al. (2008) and Dhaene et al. (2005), among others.”
Optimal approximations for risk measures of sums of lognormals based on conditional expectations (2008, background): “Since the definition (7) of S involves a conditional expectation, eliminating the randomness that cannot be explained by Λ, one may expect that S will be ‘less risky’ than S, and examining equations (12) and (13) reveals that at least the ordering of the variances supports this intuition.”
PORTFOLIO CHOICE VIA QUANTILES (2010, background): “Grigor’ev and Kan (2004) and Dhaene et al. (2005) both consider dynamic portfolio selection problems with explicitly present quantile-related criteria, but their settings are both very specific and restrictive (the former studies a discrete-time model with uniform distribution of returns, and the…”