Dynamic Stochastic Programming For Asset-liability Management

Consigli, Giorgio; Dempster, M. A. H.

doi:10.2139/ssrn.34780

Cited by 74 publications

(96 citation statements)

References 36 publications

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“…Downside-risk measures are currently used extensively in the area of ALM. Recent research typically incorporates these risk measures in a multistage stochastic programming (MSP) approach, as in Consigli and Dempster (1998), Mulvey and Thorlacius (1998), Cariño et al (1994), Boender (1997), and Dert (1998). The main advantage of the MSP approach relative to the more traditional static meanvariance oriented approach is that the explicit dynamic nature of financial decisions can better be taken into account.…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time Financial Planning Models Under Loss-Averse Preferences

Siegmann¹,

Lucas²

2005

Operations Research

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We consider a dynamic asset allocation problem formulated as a mean-shortfall model in discrete time. A characterization of the solution is derived analytically under general distributional assumptions for serially independent risky returns. The solution displays risk taking under shortfall, as well as a specific form of time diversification. Also, for a representative stock-return distribution, risk taking increases monotonically with the number of decision moments given a fixed horizon. This is related to the well-known casino effect arising in a downside-risk and expected return framework. As a robustness check, we provide results for a modified objective with a quadratic penalty on shortfall. An analytical solution for a single-stage setup is derived, and numerical results for the two-period model and time diversification are provided.Subject classifications: multistage stochastic programming; downside risk; asset/liability management; time diversification. Area of review: Financial Engineering.

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Section: Introductionmentioning

confidence: 99%

Discrete-Time Financial Planning Models Under Loss-Averse Preferences

Siegmann¹,

Lucas²

2005

Operations Research

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“…MC1Z128 and KZ2. (ii) Effects of dynamic trading and volatility pumping Multi-period models provide advantages over single-period approaches (Carino et al 1994;Consigli & Dempster 1998;Dempster et al 2003a,b where ffiffiffiffiffiffiffiffiffiffiffi ffi Mark p ðP Þ denotes the slope of the Markowitz efficient frontier when the number of trading periods is P. The non-dimensional number, Dyn(P ), quantifies the relative gain due to dynamic trading over its static counterpart when the parameters of the problem are unchanged. Table 5 shows the slopes of the Markowitz efficient frontiers for different values of the volatility of the risky asset and different numbers of trading periods.…”

Section: (I) Comparison Between Markowitz and Merton Efficient Frontiersmentioning

confidence: 99%

Markowitz principles for multi-period portfolio selection problems with moments of any order

Chellathurai

Draviam

2008

Proc. R. Soc. A.

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The multi-period portfolio selection problem is formulated as a Markowitz meanvariance optimization problem in terms of time-varying means, covariances and higherorder and intertemporal moments of the asset prices. The crux lies in expressing the number of shares of any particular asset to be transacted on any future trading date, which is a non-anticipative process, as a polynomial of the changes in the discounted prices of all the risky assets. This results in the expected return of the portfolio being dependent on not only the means of the asset prices, but also the higher-order and intertemporal moments, and its variance being dependent on not only the second-order moments, but also the higher-order and intertemporal moments. As illustrations, we study the portfolio selection problems including the discrete version of the Merton problem. It is shown numerically that the efficient frontier obtained from Markowitz's discrete multi-period formulation coincides with that from Merton's continuous-time formulation when the number of rebalancing periods is 'large'. The effects of dynamic trading, in particular volatility pumping, in comparison with a static single-period model are measured by a non-dimensional number, Dyn(P) (P, number of trading periods), which quantifies the relative gain due to dynamic trading. It is sufficient to rebalance the portfolio a few times in order to get more than 95% of the gain due to continuous trading.

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“…The stochastic programming models generally require developing a scenario tree (Kusy & Ziemba, 1986;Carino et al, 1994;Consigli & Dempster, 1998;Kouwenberg, 2001;Yu et al, 2003). The stochastic scenario tree can be considered as similar to the m-ary tree (Drmota, 2009).…”

Section: Introductionmentioning

confidence: 99%