Decisions in Economics and Finance最新文献

The state-of-the-art proposes life care annuities, that have been recently designed as variable annuity contracts with Long-Term Care payouts and Guaranteed Lifelong Withdrawal Benefits. In this paper, we propose more general features for these insurance products and refine their pricing methods. We name our proposed product “GLWB-LTC”. In particular, as to the product features, we allow dynamic withdrawal strategies, including the surrender option. Furthermore, we consider stochastic interest rates, described by a Cox–Ingersoll–Ross process. As to the numerical methods, we solve the stochastic control problem involved by the selection of the optimal withdrawal strategy through a robust tree method, which outperforms the Monte Carlo approach. We name this method “Tree-LTC”, and we use it to estimate the fair price of the product, as some relevant parameters vary, such as, for instance, the entry age of the policyholder. Furthermore, our numerical results show how the optimal withdrawal strategy varies over time with the health status of the policyholder. Our findings stress the important advantage of flexible withdrawal strategies in relation to insurance policies offering protection from health risks. Indeed, the policyholder is given more choice about how much to save for protection from the possible disability states at future times.

Let S be a metric space, (g:Srightarrow mathbb {R}) a Borel function, and ((mu _n:nge 0)) a sequence of tight probability measures on (mathcal {B}(S)). If (mu _n=mu _0) on (sigma (g)), there are S-valued random variables (X_n), all defined on the same probability space, such that (X_nsim mu _n) and (g(X_n)=g(X_0)) for all (nge 0). Moreover, (X_noverset{a.s.}{longrightarrow }X_0) if and only if (E_{mu _n}(fmid g),overset{mu _0-a.s.}{longrightarrow },E_{mu _0}(fmid g)) for each (fin C_b(S)). This result, proved in Pratelli and Rigo (J Theoret Probab 36:372-389, 2023) , is the starting point of this paper. Three types of contributions are provided. First, (sigma (g)) is replaced by an arbitrary sub-(sigma )-field (mathcal {G}subset mathcal {B}(S)). Second, the result is applied to some specific frameworks, including equivalence couplings, total variation distances, and the decomposition of cadlag processes with finhite activity. Third, following Hansen et al. (Tempered Bayesian analysis, Unpublished manuscript, 2024), the result is extended to models and kernels. This extension has a fairly natural interpretation in terms of decision theory, mass transportation and statistics.

By employing the technique of enlargement of filtrations, we demonstrate how to incorporate information about the future trend of the stochastic interest rate process into a financial model. By modeling the interest rate as an affine diffusion process, we obtain explicit formulas for the additional expected logarithmic utility in solving the optimal portfolio problem. We begin by solving the problem when the additional information directly refers to the interest rate process, and then extend the analysis to the case where the information relates to the values of an underlying Markov chain. The dynamics of this chain may depend on anticipated market information, jump at predefined epochs, and modulate the parameters of the stochastic interest rate process. The theoretical study is then complemented by an illustrative numerical analysis.

In this manuscript we provide a representation in infinite dimension for stochastic optimal control problems with delay in the control variable. The main novelty consists in the fact that the representation can be applied also to dynamics where the delay in the control appears as a nonlinear term and in the diffusion coefficient. We then apply the representation to a LQ case where an explicit solution can be found.

This piece in the series of Milestones starts from the short, clear and highly cited paper by Samuelson (Rev Econ Stat 21(2):75–78, 1939) entitled “Interactions between the Multiplier Analysis and the Principle of Acceleration”, in which the author proposes a linear dynamic model obtained by combining the Keynesian multiplier and the principle of acceleration, together with a proper structure of time lags. Although very simple, it generated a rich and interesting literature as it provides some answers to the question of endogenous business cycles. Moreover, it raises the question of sensitivity with respect to small variations of the model’s parameters, thus sparking the attention of economists and social scientists toward studies on the qualitative theory of non-linear dynamical systems, and the related work on deterministic chaos and bifurcations which appeared between the 1960 s and 1970 s, such as the paper by Lorenz (J Atmos Sci 20:130–141, 1963) in the Journal of Atmospheric Sciences or the one by May (Nature 26:459–467, 1976) in Nature, thereby stimulating an interdisciplinary mathematical approach to dynamic complexity in physics, biology and social sciences.

This work analyses expansions of exponential form for approximating probability density functions, through the utilization of diverse orthogonal polynomial bases. Notably, exponential expansions ensure the maintenance of positive probabilities regardless of the degree of skewness and kurtosis inherent in the true density function. In particular, we introduce novel findings concerning the convergence of this series towards the true density function, employing mathematical tools of functional statistics. In particular, we show that the exponential expansion is a Fourier series of the true probability with respect to a given orthonormal basis of the so called Bayesian Hilbert space. Furthermore, we present a numerical technique for estimating the coefficients of the expansion, based on the first n exact moments of the corresponding true distribution. Finally, we provide numerical examples that effectively demonstrate the efficiency and straightforward implementability of our proposed approach.

In this manuscript we consider optimal control problems of stochastic differential equations with delays in the state and in the control. First, we prove an equivalent Markovian reformulation on Hilbert spaces of the state equation. Then, using the dynamic programming approach for infinite-dimensional systems, we prove that the value function is the unique viscosity solution of the infinite-dimensional Hamilton-Jacobi-Bellman equation. We apply these results to problems coming from economics: stochastic optimal advertising problems and stochastic optimal investment problems with time-to-build.

Model averaging techniques in the actuarial literature aim to forecast future longevity appropriately by combining forecasts derived from various models. This approach often yields more accurate predictions than those generated by a single model. The key to enhancing forecast accuracy through model averaging lies in identifying the optimal weights from a finite sample. Utilizing sub-optimal weights in computations may adversely impact the accuracy of the model-averaged longevity forecasts. By proposing a game-theoretic approach employing Shapley values for weight selection, our study clarifies the distinct impact of each model on the collective predictive outcome. This analysis not only delineates the importance of each model in decision-making processes, but also provides insight into their contribution to the overall predictive performance of the ensemble.

The aim of this paper is to study optimality conditions for differentiable linearly constrained pseudoconvex programs. The stated results are based on new transversality conditions which can be used instead of complementarity ones. Necessary and sufficient optimality conditions are stated under suitable generalized convexity properties. Moreover, two different pairs of dual problems are proposed and weak and strong duality results proved. Finally, it is shown how transversality conditions can be applied to characterize optimality of convex quadratic problems and to efficiently solve a particular class of Max-Min problems

A retiree’s appetite for risk is a common input into the lifetime utility models that are traditionally used to find optimal strategies for the decumulation of retirement savings. In this work, we consider a retiree with potentially differing appetites for the key financial risks of decumulation: liquidity risk and investment risk. We set out to determine whether these differing risk appetites have a significant impact on the retiree’s optimal choice of decumulation strategy. To do so, we design and implement a framework which selects the optimal decumulation strategy from a general set of admissible strategies in line with a retiree’s goals, and under differing appetites for the key risks of decumulation. Overall, we find significant evidence to suggest that a retiree’s differing appetites for different decumulation risks will impact their optimal choice of strategy at retirement. Through an illustrative example calibrated to the Australian context, we find results which are consistent with actual behaviours in this jurisdiction (in particular, a shallow market for annuities), which lends support to our framework and may provide some new insight into the so-called annuity puzzle.