高非线性延迟随机利率模型数值解的概率收敛性
Convergence in probability of numerical solutions of a highly non-linear delayed stochastic interest rate model
AI总结：
研究高非线性延迟随机利率模型的数值解收敛性，提出分析工具，证明真实解在步长趋近于零时以概率收敛于截断欧拉-马尔可夫公式解，并通过数值实验和蒙特卡洛模拟验证结果。
摘要：
我们研究了一个具有超线性增长系数的延迟随机利率模型，并开发了新的分析工具来研究真实解及其截断欧拉-马尔可夫公式（TEM）近似解的性质。特别地，我们证明了真实解在步长趋近于零时以概率收敛于截断EM解。此外，我们通过数值实验阐明了理论发现，并利用高效的蒙特卡洛模拟框架验证了收敛结果。
英文摘要：
We study a delayed stochastic interest rate model with superlinearly growing coefficients and develop novel analytical tools to investigate the properties of both the true solution and its truncated Euler-Maruyama (TEM) approximation. In particular, we prove that the true solution converges in probability to the truncated EM solution as the step size approaches zero. Furthermore, we illustrate the theoretical findings through numerical experiments and validate the convergence results using an efficient Monte Carlo simulation framework for the valuation of relevant financial quantities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
