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Asset Price Bubbles, Wealth Preserving, Dominating and Replicating Trading Strategies

In: Peter Carr Gedenkschrift Research Advances in Mathematical Finance

Author

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  • Robert A. Jarrow
  • Yuxuan Liu

Abstract

This chapter studies an arbitrage-free, competitive and frictionless market with trading in a single risky asset and money market account, where the risky asset exhibits a price bubble. We analyze two sets of self-financing and admissible trading strategies in this market. The first are simple trading strategies, and the second are trading strategies that replicate or super-replicate the risky asset’s payoffs at the model’s horizon. We show that, in both sets, there exist wealth preserving trading strategies, i.e., trading strategies whose initial value equals the present value of their future cash flows. And, in the second set, we show that there are wealth preserving replicating trading strategies that dominate buying and holding the risky asset. The practical applications of these insights are discussed.

Suggested Citation

  • Robert A. Jarrow & Yuxuan Liu, 2023. "Asset Price Bubbles, Wealth Preserving, Dominating and Replicating Trading Strategies," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 14, pages 475-510, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811280306_0014
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    Keywords

    Mathematical Finance; Quantitative Finance; Option Pricing; Derivatives; No Arbitrage; Asset Price Bubbles; Asset Pricing; Equilibrium; Volatility; Diffusion Processes; Jump Processes; Stochastic Integration; Trading Strategies; Portfolio Theory; Optimization; Securities; Bonds; Commodities; Futures;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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