Simulation of Diversified Portfolios in a Continuous Financial Market

Platen, Eckhard; Rendek, Renata

doi:10.2139/ssrn.2170212

Cited by 9 publications

(3 citation statements)

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“…• the model can be simulated exactly -noting that the equation (4.2) is a time transformed squared Bessel process of dimension 4 [7] -using the procedure described in [62], [63], [64],…”

Section: The MMM Modelmentioning

confidence: 99%

The Asset Liability Management problem of a nuclear operator : a numerical stochastic optimization approach

Warin¹

2016

Preprint

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We numerically study an Asset Liability Management problem linked to the decommissioning of French nuclear power plants. We link the risk aversion of practitioners to an optimization problem. Using different price models we show that the optimal solution is linked to a de-risking management strategy similar to a concave strategy and we propose an effective heuristic to simulate the underlying optimal strategy. Besides we show that the strategy is stable with respect to the main parameters involved in the liability problem.

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“…• the model can be simulated exactly -noting that the equation (4.2) is a time transformed squared Bessel process of dimension 4 [7] -using the procedure described in [62], [63], [64],…”

Section: The MMM Modelmentioning

confidence: 99%

The Asset Liability Management problem of a nuclear operator : a numerical stochastic optimization approach

Warin¹

2016

Preprint

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“…In Platen and Rendek (2010), the authors perform a detailed simulation study on the effect of diversification for a range of market models beyond the standard market model.…”

Section: Simulation Of a Standard Market Modelmentioning

confidence: 99%

Approximating the numéraire portfolio by naive diversification

Platen

Rendek

2011

J Asset Manag

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Abstract. Estimation theory has shown, due to the limited estimation window available for real asset data, the sample based Markowitz mean-variance approach produces unreliable weights which fluctuate substantially over time. This paper proposes an alternate approach to portfolio optimization, being the use of naive diversification to approximate the numéraire portfolio. The numéraire portfolio is the strictly positive portfolio that, when used as benchmark, makes all benchmarked nonnegative portfolios either mean decreasing or trendless. Furthermore, it maximizes expected logarithmic utility and outperforms any other strictly positive portfolio in the long run. The paper proves for a well-securitized market that the naive equal value weighted portfolio converges to the numéraire portfolio when the number of constituents tends to infinity. This result is model independent and, therefore, very robust. The systematic construction of diversified stock indices by naive diversification from real data is demonstrated. Even when taking transaction costs into account, these indices significantly outperform the corresponding market capitalization weighted indices in the long run, indicating empirically their asymptotic proximity to the numéraire portfolio. Finally, in time of financial crisis, a large equi-weighted fund carrying the investments of major pension funds and insurance companies would provide important liquidity. It would not only dampen the drawdown of a crisis but would also moderate the excesses of an asset price bubble.

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“…The well-established literature on optimal growth considers portfolio weights chosen to maximize the expected geometric growth rate of the portfolio value, consistent with maximizing the expected logarithm of final wealth (Kelly, 1956;Luenberger, 1997;Thorp, 2010;Platen and Rendek, 2010). Rebalancing is a vital part of these strategies.…”

Section: Introductionmentioning

confidence: 99%