Explaining Diversities in Age-Specific Life Expectancies and Values of Life Saving: A Numerical Analysis

Little attempt has been made so far to quantify the extent to which individual willingness to spend on life protection may account for the observed trends and diversities in agespecific life expectancies across individuals and over time. We address these issues via calibrated simulations of a dynamic, life-cycle model of life protection in which life's end is a stochastic event, age-specific mortality risks are endogenous variables, and spending on life protection is set jointly with related insurance options: life insurance as well as annuities. A unique feature of our model is that it links age-specific mortality risks and implicit private values-of-life-saving (VLS) as "dual variables", and estimates them jointly. It also offers new insights about the concept and measurement of VLS. Life protection is estimated to have a non-negligible impact on age-specific life expectancies. It can account for significant portions of observed inequalities in life expectancies across population groups and over time, as well as for a wide range of empirical estimates of VLS produced via the conventional "willingness to pay" approach.

Design of generalized fractional order gradient descent method

This paper focuses on the convergence problem of the emerging fractional order gradient descent method, and proposes three solutions to overcome the problem. In fact, the general fractional gradient method cannot converge to the real extreme point of the target function, which critically hampers the application of this method. Because of the long memory characteristics of fractional derivative, fixed memory principle is a prior choice. Apart from the truncation of memory length, two new methods are developed to reach the convergence. The one is the truncation of the infinite series, and the other is the modification of the constant fractional order. Finally, six illustrative examples are performed to illustrate the effectiveness and practicability of proposed methods.Comment: 8 pages, 16 figure

Description and Realization for a Class of Irrational Transfer Functions

This paper proposes an exact description scheme which is an extension to the well-established frequency distributed model method for a class of irrational transfer functions. The method relaxes the constraints on the zero initial instant by introducing the generalized Laplace transform, which provides a wide range of applicability. With the discretization of continuous frequency band, the infinite dimensional equivalent model is approximated by a finite dimensional one. Finally, a fair comparison to the well-known Charef method is presented, demonstrating its added value with respect to the state of art.Comment: 9 pages, 9 figure