标题： 从累计违约概率确定信用转移矩阵 显示英文标题

标题： Determining a credit transition matrix from cumulative default probabilities

摘要： 量化债券信用评级的变化是信用评级行业的一个重要数学问题。 将信用评级视为马尔可夫链的状态是一个有趣的提议，这导致了数学建模中的挑战。 由于累计违约率比信用迁移更容易测量，一个自然的问题是，是否可以从累计违约概率的知识中确定信用转移矩阵（CTM）。 在这里，我们利用CTM与累计违约概率之间的关系，建立了一个带有箱约束的不适定线性逆问题，我们通过熵最小化过程来解决这个问题。 这种方法在多个方面都具有吸引力。 一方面，我们可能拥有比未知数更少的数据，另一方面，即使我们拥有的数据与未知数数量相同，连接它们的矩阵也可能不可逆，这使得问题变得不适定。 除了开发解决该问题的工具外，我们还将其应用于几个测试案例，以检查该方法的性能。 结果非常令人满意。 显示英文摘要

摘要： To quantify the changes in the credit rating of a bond is an important mathematical problem for the credit rating industry. To think of the credit rating as the state a Markov chain is an interesting proposal leading to challenges in mathematical modeling. Since cumulative default rates are more readily measurable than credit migrations, a natural question is whether the credit transition matrix (CTM) can be determined from the knowledge of the cumulative default probabilities. Here we use a connection between the CTM and the cumulative default probabilities to setup an ill-posed, linear inverse problem with box constraints, which we solve by an entropy minimization procedure. This approach is interesting on several counts. On the one hand, we may have less data that unknowns, and on the other hand, even when we have as much data as unknowns, the matrix connecting them may not be invertible, which makes the problem ill-posed. Besides developing the tools to solve the problem, we apply it to several test cases to check the performance of the method. The results are quite satisfactory.