In the process of loan pricing, stress testing, capital allocation, modeling of PD term structure, and IFRS9 expected credit loss estimation, it is widely expected that higher risk grades carry higher default risks, and that an entity is more likely to migrate to a closer non-default rating than...

Common ordinal models, including the ordered logit model and the continuation ratio model, are structured by a common score (i.e., a linear combination of a list of given explanatory variables) plus rank specific intercepts. Sensitivity with respect to the common score is generally not...

Most point-in-time PD term structure models used in industry for stress testing and IFRS9 expected loss estimation apply only to macroeconomic scenarios. Loan level credit quality is not a factor in these models. In practice, credit profile at assessment time plays an important role in the...

Monotonic estimation for the survival probability of a loan in a risk-rated portfolio is based on the observation arising, for example, from loan pricing that a loan with a lower credit risk rating is more likely to survive than a loan with a higher credit risk rating, given the same additional...

Minimum cross-entropy estimation is an extension to the maximum likelihood estimation for multinomial probabilities. Given a probability distribution {r_i }_(i=1)^k, we show in this paper that the monotonic estimates {p_i }_(i=1)^k for the probability distribution by minimum cross-entropy are...

In the society utility is the vital concept, especially in mathematical economics. It is considered as the tendency of an object or action that increases or decreases overall happiness. In social sciences, the property of a commodity that enables to satisfy human wants is called utility. This...

In this paper sensitivity analysis between Lagrange multipliers and total budget is discussed. The method of Lagrange multipliers is a very useful and powerful technique in multivariable calculus. In mathematical economics, utility is the vital concept that increases or decreases overall...

Every local or global firm expects to achieve maximum profit for its survival in sustainable economic environment. This article considers that a local industrial firm of Bangladesh has achieved maximum profit during its total operation. So that this study directly tries to calculate maximum...

In this study method of Lagrange multiplier is considered to investigate profit maximization policy. In the twenty first century global economy faces serious complexities. Sensitivity analysis of economic firms becomes essential part of sustainable economic environment. The method of Lagrange...