英文标题：
《Optimal Investment and Pricing in the Presence of Defaults》
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作者：
Tetsuya Ishikawa, Scott Robertson
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最新提交年份：
2017
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英文摘要：
We consider the optimal investment problem when the traded asset may default, causing a jump in its price. For an investor with constant absolute risk aversion, we compute indifference prices for defaultable bonds, as well as a price for dynamic protection against default. For the latter problem, our work complements Sircar & Zariphopoulou (2007), where it is implicitly assumed the investor is protected against default. We consider a factor model where the asset\'s instantaneous return, variance, correlation and default intensity are driven by a time-homogenous diffusion X taking values in an arbitrary region E. We identify the certainty equivalent with a semi-linear degenerate elliptic partial differential equation with quadratic growth in both function and gradient. Under a minimal integrability assumption on the market price of risk, we show the certainty equivalent is a classical solution. In particular, our results cover when X is a one-dimensional affine diffusion and when returns, variances and default intensities are also affine. Numerical examples highlight the relationship between the factor process and both the indifference price and default insurance. Lastly, we show the insurance protection price is not the default intensity under the dual optimal measure.
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中文摘要：
我们考虑当交易资产可能违约，导致其价格上涨时的最优投资问题。对于具有恒定绝对风险厌恶的投资者，我们计算了可违约债券的无差异价格，以及动态违约保护的价格。对于后一个问题，我们的工作补充了Sircar&Zariphopoulou（2007），其中隐含地假设投资者受到违约保护。我们考虑一个因子模型，其中资产的瞬时收益、方差、相关性和违约强度由时间齐次扩散X驱动，X取任意区域E中的值。我们确定确定性等价于函数和梯度均为二次增长的半线性退化椭圆型偏微分方程。在风险市场价格的最小可积性假设下，我们证明了确定性等价是一个经典解。特别是，我们的结果涵盖了当X是一维仿射扩散时，以及当收益、方差和默认强度也是仿射时。数值例子突出了因子过程与无差异价格和违约保险之间的关系。最后，我们证明了在双重最优测度下，保险保护价格不是违约强度。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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