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Mean-Variance Asset-Liability Management Problem Under Non-Markovian Regime-Switching Models

机译:非马洛维亚政权切换模型下的平均值资产资产负债管理问题

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摘要

In this paper, we study an asset-liability management problem under a mean-variance criterion with regime switching. Unlike previous works, the dynamics of assets and liability are described by non-Markovian regime-switching models in the sense that all the model parameters are predictable with respect to the filtration generated jointly by a Markov chain and a Brownian motion. The problem is solved with the aid of backward stochastic differential equations (BSDEs) and bounded mean oscillation martingales. An efficient strategy and an efficient frontier are obtained and represented by unique solutions to several relevant BSDEs. We show that the optimal capital structure can be achieved when the initial asset value is expressed by a linear combination of the initial liability and the expected surplus. It is further found that a mutual fund theorem holds not only for the efficient strategy, but also for the optimal capital structure.
机译:在本文中,我们在具有政权切换的平均方差标准下研究了资产负债管理问题。 与以前的作品不同,资产和责任的动态由非马洛维亚政权 - 切换模型描述,意义上,所有模型参数都是可预测的,即在马尔可夫链和布朗运动中共同产生的过滤。 借助于向后随机微分方程(BSDES)和有界平均振荡Martingales来解决问题。 获得有效的策略和高效的前沿,并通过唯一的解决方案来表示几个相关的BSDE。 我们表明,当初始资产值用初始责任的线性组合和预期的剩余表示时,可以实现最佳资本结构。 进一步发现,共同基金定理不仅适用于有效的策略,而且还具有最佳资本结构。

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