scholarly journals Fair Valuation of Insurance Liability Cash-Flow Streams in Continuous Time: Applications

2018 ◽  
Author(s):  
Lukasz Delong ◽  
Jan Dhaene ◽  
Karim Barigou
Keyword(s):  
Cash Flow ◽  
Continuous Time ◽  
Fair Valuation

scholarly journals FAIR VALUATION OF INSURANCE LIABILITY CASH-FLOW STREAMS IN CONTINUOUS TIME: APPLICATIONS

2019 ◽  
Vol 49 (2) ◽  
pp. 299-333 ◽  
Author(s):  
Łukasz Delong ◽  
Jan Dhaene ◽  
Karim Barigou
Keyword(s):  
Cash Flow ◽  
Continuous Time ◽  
Financial Risk ◽  
Explicit Solutions ◽  
Financial Risks ◽  
Practical Applications ◽  
Risk Margin ◽  
Hedging Strategies ◽  
Fair Market ◽  
Fair Valuation

AbstractDelong et al. (2018) presented a theory of fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. In this paper, we investigate in detail two practical applications of our theory of fair valuation. In the first example, we consider the fair valuation of a terminal benefit which is contingent on correlated tradeable and non-tradeable financial risks. In the second example, we consider a portfolio of unit-linked contracts contingent on a non-tradeable insurance and a tradeable financial risk. We derive partial differential equations (PDEs) which characterize the continuous-time fair valuation operators in these two examples and we find explicit solutions to these PDEs. The fair values of the liabilities are decomposed into the best estimate of the liability and a risk margin. The arbitrage-free representations of the fair values of the liabilities are derived and the dynamic hedging strategies associated with the continuous-time fair valuation operators are also established. Detailed interpretations of the results, which should be useful both for researchers and practitioners, are provided.

scholarly journals Usefulness of fair valuation of biological assets for cash flow prediction

2017 ◽  
Vol 47 (2) ◽  
pp. 157-180 ◽  
Author(s):  
Josep Maria Argilés-Bosch ◽  
Meritxell Miarons ◽  
Josep Garcia-Blandon ◽  
Carmen Benavente ◽  
Diego Ravenda
Keyword(s):  
Cash Flow ◽  
Flow Prediction ◽  
Fair Valuation

scholarly journals Stochastic continuous-time cash flows: A coupled linear-quadratic model

2021 ◽  
Author(s):  
◽  
Johannus Gerardus Josephus Van der Burg
Keyword(s):  
Density Function ◽  
Cash Flow ◽  
Continuous Time ◽  
Cash Flows ◽  
Quadratic Model ◽  
Linear Quadratic ◽  
Fundamental Model ◽  
Linear Quadratic Model ◽  
Flow Processes ◽  
Operating Cash Flow

<p>The focal point of this dissertation is stochastic continuous-time cash flow models. These models, as underpinned by the results of this study, prove to be useful to describe the rich and diverse nature of trends and fluctuations in cash flow randomness. Firstly, this study considers an important preliminary question: can cash flows be fully described in continuous time? Theoretical and empirical evidence (e.g. testing for jumps) show that under some not too stringent regularities, operating cash flow processes can be well approximated by a diffusion equation, whilst investing processes -preferably- will first need to be rescaled by a system-size variable. Validated by this finding and supported by a multitude of theoretical considerations and statistical tests, the main conclusion of this dissertation is that an equation consisting of a linear drift function and a complete quadratic diffusion function (hereafter: “the linear-quadratic model”) is a specification preferred to other specifications frequently found in the literature. These so-called benchmark processes are: the geometric and arithmetic Brownian motions, the mean-reverting Vasicek and Cox, Ingersoll and Ross processes, and the modified Square Root process. Those specifications can all be considered particular cases of the generic linear-quadratic model. The linear-quadratic model is classified as a hybrid model since it is shown to be constructed from the combination of geometric and arithmetic Brownian motions. The linear-quadratic specification is described by a fundamental model, rooted in well-studied and generally accepted business and financial assumptions, consisting of two coupled, recursive relationships between operating and investing cash flows. The fundamental model explains the positive feedback mechanism assumed to exist between the two types of cash flows. In a stochastic environment, it is demonstrated that the linear-quadratic model can be derived from the principles of the fundamental model. There is no (known) general closed-form solution to the hybrid linear-quadratic cash flow specification. Nevertheless, three particular and three approximated exact solutions are derived under not too stringent parameter restrictions and cash flow domain limitations. Weak solutions are described by (forward or backward) Fokker-Planck- Kolmogorov equations. This study shows that since the process is converging in time (that is, approximating a stable probability distribution), (uncoupled) investing cash flows can be described by a Pearson diffusion process approaching a stationary Person-IV probability density function, more appropriately a Student diffusion process. In contrast, (uncoupled) operating cash flow processes are diverging in time, that is exploding with no stable probability density function, a dynamic analysis in a bounded cash flow domain is required. A suggested solution method normalises a general hypergeometric differential equation, after separation of variables, which is then transformed into a Sturm-Liouville specification, followed by a choice of three separate second transformations. These second transformations are the Jacobi, the Hermitian and the Schrödinger, each yielding a homonymous equation. Only the Jacobi transformation provides an exact solution, the other two transformations lead to approximated closed-form general solutions. It turns out that a space-time density function of operating cash flow processes can be construed as the multiplication of two (independent) time-variant probability distributions: a stationary family of distributions akin to Pearson’s case 2, and the evolution of a standard normal distribution. The fundamental model and the linear-quadratic specification are empirically validated by three different statistical tests. The first test provides evidence that the fundamental model is statistically significant. Parameter values support the conclusion that operating and investing processes are converging to overall long-term stable values, albeit with significant stochastic variation of individual firms around averages. The second test pertains to direct estimation from approximated SDE solutions. Parameter values found, are not only plausible but agree with theoretical considerations and empirical observations elaborated in this study. The third test relates to an approximated density function and its associated approximated maximum likelihood estimator. The Ait-Sahalia- method, in this study adapted to derive the Fourier coefficients (of the Hermite expansion) from a (closed) system of moment ODEs, is considered a superior technique to derive an approximated density function associated with the linear-quadratic model. The maximum likelihood technique employed, proper for high-parametrised estimations, includes re-parametrisation (based on the extended invariance principle) and stepwise maximisation. Reported estimation results support the hypothesised superiority of the linear-quadratic cash flow model, either in complete (five-parameter form) or in a reduced-parameter form, in comparison to the examined five benchmark processes.</p>

scholarly journals Laplace, Hansen-Sargent and Beveridge-Nelson a note towards unified business application

2021 ◽  
Vol 16 (1) ◽  
pp. 39-47
Author(s):  
Vladimir Andrić ◽  
Sanja Nenadović
Keyword(s):  
Corporate Finance ◽  
Cash Flow ◽  
Continuous Time ◽  
Laplace Transforms ◽  
Present Value ◽  
Prediction Formula ◽  
Cycle Decomposition ◽  
Business Application ◽  
Equivalence Condition

The paper derives the equivalence condition between the Beveridge-Nelson decomposition and the Hansen-Sargent prediction formula in continuous time using Laplace transforms. The results presented show how the Hansen-Sargent prediction formula is relevant not just for present value discounting but also for the trend-cycle decomposition of cash flow streams in corporate finance.

scholarly journals Continuous-time limits of multi-period cost-of-capital margins

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hampus Engsner ◽  
Filip Lindskog
Keyword(s):  
Cash Flow ◽  
Discrete Time ◽  
Continuous Time ◽  
Cost Of Capital ◽  
Limited Liability ◽  
Cash Flows ◽  
Capital Requirements ◽  
Time Cost ◽  
Time Limits ◽  
Capital Injections

AbstractWe consider multi-period cost-of-capital valuation of a liability cash flow subject to repeated capital requirements that are partly financed by capital injections from capital providers with limited liability. Limited liability means that, in any given period, the capital provider is not liable for further payment in the event that the capital provided at the beginning of the period turns out to be insufficient to cover both the current-period payments and the updated value of the remaining cash flow. The liability cash flow is modeled as a continuous-time stochastic process on {[0,T]}. The multi-period structure is given by a partition of {[0,T]} into subintervals, and on the corresponding finite set of times, a discrete-time cost-of-capital-margin process is defined. Our main objective is the analysis of existence and properties of continuous-time limits of discrete-time cost-of-capital-margin processes corresponding to a sequence of partitions whose meshes tend to zero. Moreover, we provide explicit expressions for the limit processes when cash flows are given by Itô diffusions and processes with independent increments.

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