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首页> 外文期刊>Theory and Decision >Risk-adjusted martingales and the design of 'Indifference' gambles
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Risk-adjusted martingales and the design of 'Indifference' gambles

机译：风险调整型mar和“无差异”赌博的设计

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摘要

In the probability literature, a martingale is often referred to as a "fair game." A martingale investment is a stochastic sequence of wealth levels, whose expected value at any future stage is equal to the investor's current wealth. In decision theory, a risk neutral investor would therefore be indifferent between holding on to a martingale investment, and receiving its payoff at any future stage, or giving it up and maintaining his current wealth. But a risk-averse decision maker would not be indifferent between a martingale investment and his current wealth level, since he values uncertain deals less than their mean. A risk seeking decision maker, on the other hand, would readily accept a martingale investment in exchange for his current wealth, and would repeat this investment any number of times. These ideas lead us to introduce the notion of a "risk-adjusted martingale"; a stochastic sequence of wealth levels that a rational decision maker with any attitude toward risk would value constantly with time, and would be indifferent between receiving its pay-off at any future stage, or giving it up and maintaining his current wealth level. We show how to construct such risk-adjusted investments for any decision maker with a continuous monotonic utility function. The fundamental result we derive is that a pay-off structure of an investment (i) is a risk-adjusted martingale and (ii) can be represented by a lattice if and only if the pay-off functions are invariant transformations of the given utility function.
机译：在概率文献中，a通常被称为“公平博弈”。 mar投资是财富水平的随机序列，其在任何未来阶段的预期价值都等于投资者的当前财富。因此，在决策理论中，风险中立的投资者在持有a投资，在任何未来阶段获得回报，或放弃并保持其当前财富之间都将是无关紧要的。但是，一个规避风险的决策者对mar投资和他目前的财富水平不会感到冷漠，因为他对不确定的交易的重视程度低于平均水平。另一方面，寻求风险的决策者会轻易接受ting投资以换取他目前的财富，并且会重复多次该投资。这些想法使我们引入了“风险调整mar”的概念；理性地对风险采取任何态度的理性决策者会随着时间的推移不断地评估财富水平的随机序列，而在以后的任何阶段获得回报，放弃或维持当前的财富水平之间，都将无动于衷。我们展示了如何为具有连续单调效用函数的任何决策者构建这种经过风险调整的投资。我们得出的基本结果是，一项投资的收益结构（i）是经过风险调整的mar，并且（ii）当且仅当收益函数是给定效用的不变变换时，才能用格表示。功能。

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  • 来源
    《Theory and Decision》 |2011年第4期|p.643-668|共26页
  • 作者

    Ali E. Abbas;

  • 作者单位

    Department of Industrial and Enterprise Systems Engineering, College of Engineering,University of Illinois at Urbana-Champaign, 104 S. Mathews Ave, Urbana, IL 61820, USA;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    martingales; risk aversion; invariance; expected utility;

    机译：ting;风险规避;不变性;预期效用;

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