<p>This paper investigates ambiguity aversion in the context of a utility-maximizing investor operating under the LVO-CEV model, which is a novel extension within the Constant Elasticity of Variance (CEV) framework. By embedding a relative entropy penalty, we derive closed-form solutions for optimal portfolio exposure, asset allocation, and consumption under Hyperbolic Absolute Risk Aversion (HARA) utility. These solutions provide clear insights into how ambiguity aversion interacts with key model parameters to shape optimal investment and consumption decisions. We further analyze two representative investor types who adopt commonly observed suboptimal strategies with consumption and quantify their associated utility losses using the Wealth-Equivalent Loss (WEL) metric. Empirically, based on estimates on historical S&P 500 index data, we find that in the non-robust case (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\phi =0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϕ</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>), the optimal asset allocation peaks at approximately 61%. Under ambiguity-aversion (e.g., <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\phi = 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϕ</mi> <mo>=</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>), this value declines to around 30%, highlighting the substantial impact of ambiguity on portfolio choice. The proportional reduction is shown to be independent of the size of the CEV parameter <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>. Furthermore, our analysis of wealth-equivalent losses indicates that neglecting ambiguity aversion or wealth-floor constraints can lead to significant utility losses. For instance, disregarding ambiguity aversion alone (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\phi = 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϕ</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>) results in an approximate 8% wealth-equivalent loss at <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\phi = 10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϕ</mi> <mo>=</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation> over an eight-year horizon, and this loss rises to approximately 13% when the wealth-floor constraint is also omitted (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\phi = 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϕ</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$F = 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>F</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>). Overall, these findings underscore the importance of robust and integrated portfolio strategies that explicitly account for ambiguity, investor risk preferences, and consumption dynamics in long-term investment planning.</p>

Robust portfolio optimization within the LVO-CEV model

期刊论文
发表日期：

2026年6月28日

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Marcos Escobar-Anel,
Wei Li Fan

摘要

This paper investigates ambiguity aversion in the context of a utility-maximizing investor operating under the LVO-CEV model, which is a novel extension within the Constant Elasticity of Variance (CEV) framework. By embedding a relative entropy penalty, we derive closed-form solutions for optimal portfolio exposure, asset allocation, and consumption under Hyperbolic Absolute Risk Aversion (HARA) utility. These solutions provide clear insights into how ambiguity aversion interacts with key model parameters to shape optimal investment and consumption decisions. We further analyze two representative investor types who adopt commonly observed suboptimal strategies with consumption and quantify their associated utility losses using the Wealth-Equivalent Loss (WEL) metric. Empirically, based on estimates on historical S&P 500 index data, we find that in the non-robust case ( $\phi =0$ $ϕ = 0$ ), the optimal asset allocation peaks at approximately 61%. Under ambiguity-aversion (e.g., $\phi = 3$ $ϕ = 3$ ), this value declines to around 30%, highlighting the substantial impact of ambiguity on portfolio choice. The proportional reduction is shown to be independent of the size of the CEV parameter $\beta $ $β$ . Furthermore, our analysis of wealth-equivalent losses indicates that neglecting ambiguity aversion or wealth-floor constraints can lead to significant utility losses. For instance, disregarding ambiguity aversion alone ( $\phi = 0$ $ϕ = 0$ ) results in an approximate 8% wealth-equivalent loss at $\phi = 10$ $ϕ = 10$ over an eight-year horizon, and this loss rises to approximately 13% when the wealth-floor constraint is also omitted ( $\phi = 0$ $ϕ = 0$ , $F = 0$ $F = 0$ ). Overall, these findings underscore the importance of robust and integrated portfolio strategies that explicitly account for ambiguity, investor risk preferences, and consumption dynamics in long-term investment planning.