SSRN Author: Martin HerdegenMartin Herdegen SSRN Content
https://privwww.ssrn.com/author=2157223
https://privwww.ssrn.com/rss/en-usWed, 21 Jul 2021 01:40:12 GMTeditor@ssrn.com (Editor)Wed, 21 Jul 2021 01:40:12 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Mean-ρ portfolio selection and ρ-arbitrage for coherent risk measuresWe revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure ρ. We first show that under mild assumptions, the set of optimal portfolios for a fixed return is nonempty and compact. However, unlike in classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation ρ-arbitrage, and prove that it cannot be excluded -- unless ρ is as conservative as the worst-case risk measure.<br><br>After providing a primal characterisation of ρ-arbitrage, we focus our attention on coherent risk measures that admit a dual representation and give a necessary and sufficient dual characterisation of ρ-arbitrage. We show that the absence of ρ-arbitrage is intimately linked to the interplay between the set of equivalent martingale measures (EMMs) for the discounted risky assets and the set of absolutely continuous measures in the dual representation of ρ. A special case ...
https://privwww.ssrn.com/abstract=3691027
https://privwww.ssrn.com/2043809.htmlTue, 20 Jul 2021 18:36:18 GMTREVISION: An Elementary Approach to the Merton ProblemIn this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black-Scholes-Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write down a candidate value function and to use a verification argument to prove that this is the solution to the problem. However, features of the problem take it outside the standard settings of stochastic control, and the existing primal verification proofs rely on parameter restrictions (especially, but not only, R<1), restrictions on the space of admissible strategies, or intricate approximation arguments.<br><br>The purpose of this paper is to show that these complications can be overcome using a simple and elegant argument involving a stochastic perturbation of the utility function.
https://privwww.ssrn.com/abstract=3623047
https://privwww.ssrn.com/2009377.htmlTue, 30 Mar 2021 11:14:28 GMTREVISION: Mean-ρ portfolio selection and ρ-arbitrage for coherent risk measuresWe revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure ρ. We first show that under mild assumptions, the set of optimal portfolios for a fixed return is nonempty and compact. However, unlike in classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation ρ-arbitrage, and prove that it cannot be excluded -- unless ρ is as conservative as the worst-case risk measure.<br><br>After providing a primal characterisation of ρ-arbitrage, we focus our attention on coherent risk measures that admit a dual representation and give a necessary and sufficient dual characterisation of ρ-arbitrage. We show that the absence of ρ-arbitrage is intimately linked to the interplay between the set of equivalent martingale measures (EMMs) for the discounted risky assets and the set of absolutely continuous measures in the dual representation of ρ. A special case ...
https://privwww.ssrn.com/abstract=3691027
https://privwww.ssrn.com/2003817.htmlThu, 18 Mar 2021 08:35:45 GMTREVISION: A Dual Characterisation of Regulatory Arbitrage for Coherent Risk MeasuresWe revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure ρ on L1. We first show that under mild assumptions, the set of optimal portfolios for a fixed return is nonempty and compact. However, unlike in classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation regulatory arbitrage, and prove that it cannot be excluded – unless ρ is as conservative as the worst-case risk measure.<br><br>After providing a primal characterization, we focus our attention on coherent risk measures, and give a necessary and sufficient characterization for regulatory arbitrage. We show that the presence or absence of regulatory arbitrage for ρ is intimately linked to the interplay between the set of equivalent martingale measures (EMMs) for the discounted risky assets and the set of absolutely continuous measures in the dual representation of ρ. A special case of ...
https://privwww.ssrn.com/abstract=3691027
https://privwww.ssrn.com/1957670.htmlMon, 02 Nov 2020 12:08:32 GMTREVISION: Equilibrium Asset Pricing with Transaction CostsWe study risk-sharing economies where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled forward-backward stochastic differential equations. We show that a unique solution generally exists provided that the agents' preferences are sufficiently similar. In a benchmark specification with linear state dynamics, the illiquidity discounts and liquidity premia observed empirically correspond to a positive relationship between transaction costs and volatility.<br>
https://privwww.ssrn.com/abstract=3326085
https://privwww.ssrn.com/1946434.htmlWed, 30 Sep 2020 09:49:51 GMT