Multi-Asset Worst-Case Optimal Portfolios

Korn, Ralf; Leoff, Elisabeth

doi:10.1142/s0219024919500195

Cited by 7 publications

(8 citation statements)

References 8 publications

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“…where we use the notation (z, ξ) instead of (z (1) , ξ 1 ). As this problem was discussed in detail in [9], we only recall ideas and results, and introduce essential concepts.…”

Section: The One-stress Worst-case Problemmentioning

confidence: 99%

“…Now we can introduce the second essential concept, the indifference frontier. For a proof of the following multi-asset statement we refer to [9]. Proposition 4 (Indifference frontier) Let Assumption (2) be valid and let π ∈ A(x) be an admissible portfolio process for the one-stress worst-case portfolio problem with stress scenario (z, ξ).…”

Section: Definitionmentioning

confidence: 99%

“…In the course of this work, we will see in particular that the portfolio optimization problems considered in [12] and [9], among others, are in fact special cases of the problem introduced here. More precisely, we have generalised the problem with one stock and n ≥ 1 identical stresses stated in [12].…”

Section: Introductionmentioning

confidence: 98%

“…More precisely, we have generalised the problem with one stock and n ≥ 1 identical stresses stated in [12]. Also, our model includes the multi-asset problem with one stress in [9] as a simple special case.…”

Section: Introductionmentioning

confidence: 99%

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Optimal portfolios in the presence of stress scenarios A worst-case approach

Korn

Müller

2021

Math Finan Econ

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Insurance companies and banks regularly have to face stress tests performed by regulatory instances. To model their investment decision problems that includes stress scenarios, we propose the worst-case portfolio approach. Thus, the resulting optimal portfolios are already stress test prone by construction. A central issue of the worst-case portfolio approach is that neither the time nor the order of occurrence of the stress scenarios are known. Even more, there are no probabilistic assumptions regarding the occurrence of the stresses. By defining the relative worst-case loss and introducing the concept of minimum constant portfolio processes, we generalize the traditional concepts of the indifference frontier and the indifference-optimality principle. We prove the existence of a minimum constant portfolio process that is optimal for the multi-stress worst-case problem. As a main result we derive a verification theorem that provides conditions on Lagrange multipliers and nonlinear ordinary differential equations that support the construction of optimal worst-case portfolio strategies. The practical applicability of the verification theorem is demonstrated via numerical solution of various worst-case problems with stresses. There, it is in particular shown that an investor who chooses the worst-case optimal portfolio process may have a preference regarding the order of stresses, but there may also be stress scenarios where he/she is indifferent regarding the order and time of occurrence.

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“…where we use the notation (z, ξ) instead of (z (1) , ξ 1 ). As this problem was discussed in detail in [9], we only recall ideas and results, and introduce essential concepts.…”

Section: The One-stress Worst-case Problemmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal portfolios in the presence of stress scenarios A worst-case approach

Korn

Müller

2021

Math Finan Econ

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“…Further approaches include, among a host of other concepts, robust portfolio optimization (Kim et al 2014), regime-switching models ( Bäuerle and Rieder (2004), Haussmann and Sass (2004), Krishnamurthy et al (2018) or worst-case portfolio optimization ( Korn and Wilmott (2002), Seifried (2010), Korn and Leoff (2019)). An overview of practical challenges and future trends is given in Kolm et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Multicriteria asset allocation in practice

et al. 2021

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In this paper, we consider the strategic asset allocation of an insurance company. This task can be seen as a special case of portfolio optimization. In the 1950s, Markowitz proposed to formulate portfolio optimization as a bicriteria optimization problem considering risk and return as objectives. However, recent developments in the field of insurance require four and more objectives to be considered, among them the so-called solvency ratio that stems from the Solvency II directive of the European Union issued in 2009. Moreover, the distance to the current portfolio plays an important role. While the literature on portfolio optimization with three objectives is already scarce, applications in the financial context with four and more objectives have not yet been solved so far by multi-objective approaches based on scalarizations. However, recent algorithmic improvements in the field of exact multi-objective methods allow the incorporation of many objectives and the generation of well-spread representations within few iterations. We describe the implementation of such an algorithm for a strategic asset allocation with four objective functions and demonstrate its usefulness for the practitioner. Our approach is in operative use in a German insurance company. Our partners report a significant improvement in their decision-making process since, due to the proper integration of the new objectives, the software proposes portfolios of much better quality than before within short running time.

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Optimal Portfolios for Large Investors in Housing Markets Under Stress Scenarios: A Worst-Case Approach

Yilmaz

2024

Comput Econ

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The study focuses on constructing a mathematical housing market threatened by a major catastrophic event or crash. It incorporates the worst-case scenario portfolio optimization problem as introduced in Korn and Wilmott (Int J Theor Appl Finance 5(02):171–187, 2002) into housing markets. The standard stochastic models for housing markets assume a geometric Brownian motion and neglect sudden housing price falls during crash times. However, the size, timing, and frequency of crashes have to be included in such models. By incorporating the worst-case portfolio optimization problem into housing markets, this study introduces a methodology to construct portfolios for large investors that are robust and resilient to extreme housing market conditions. The worst-case portfolio optimization approach can be used in housing markets to incorporate stress scenarios, minimize potential losses, utilize mathematical techniques, and manage housing investment risk effectively. This study provides valuable insights for large investors seeking to construct housing portfolios prioritizing downside protection and minimizing losses in extreme housing market conditions. Utilizing numerical illustrations, it provides insights into portfolio construction, demonstrating the effectiveness of adjusting portfolios to mitigate downside risks during housing market crises. The results highlight dynamic portfolio management’s significance in safeguarding wealth when housing prices undergo significant fluctuations.

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Multi-Asset Worst-Case Optimal Portfolios

Cited by 7 publications

References 8 publications

Optimal portfolios in the presence of stress scenarios A worst-case approach

Optimal portfolios in the presence of stress scenarios A worst-case approach

Multicriteria asset allocation in practice

Optimal Portfolios for Large Investors in Housing Markets Under Stress Scenarios: A Worst-Case Approach

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