Questions tagged [actuarial-science]
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13 questions
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Deferred mortality probabilities (mortality table)
My question has to do with drawing correct conclusions regarding deferred mortality probability from a mortality table.
I am looking at the table below (source). In it, the $q_x$ (2nd columns) is ...
- 101
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97
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Reserves using Thiele differential equation
I am trying to solve the Thiele differential equations
$$
\frac{d}{dt}V^1(t)=r(t)V^1(t)-b^1(t)-\mu_{12}(t)(V^2(t)-V^1(t))-\mu_{10}(t)(V^1(t)) \\
\frac{d}{dt}V^2(t)=r(t)V^2(t)-\mu_{21}(t)(V^1(t)-V^2(t))...
- 11
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Cohort-based model vs. population-based model for mortality
A cohort-based model groups individuals with at least one common characteristic over a period of time through a state-transition process. A population-based model reflects as much information as ...
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Is it possible to have negative beta terms in the Nelson-Siegel model?
The Nelson-Siegel model as described in this paper has the following form:
$$ y_t(\tau) = \beta_0 + \frac{(\beta_1+\beta_2)(1- e^{(-m/\tau)})}{\frac{m}{\tau}} - \beta_2e^{(-m/\tau)}
$$
Can the $\...
- 161
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Instantaneous Forward LIBOR rate formula under the real-world measure: A fundamental question
We know how the formula of an instantaneous forward LIBOR rate looks like:
\begin{eqnarray}
L(t, t, T) = \frac{1}{\Delta}\left(\frac{1}{P(t, T)} -1\right)
\end{eqnarray}
where $P(t, T)$ stands for the ...
- 419
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Poisson distributed claim in non life insurance mathematics
I am struggling with the following problem. I assume that there is a single claim number $X$ with corresponding heterogeneity parameter $\theta>0$.
I assume that $X$ given $\theta$ is Poisson ...
- 115
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Poisson modelling of non-life insurance claims with reporting delay
I am considering a portfolio of car insurance policies. In order to capture the individual history (driving skills, age, etc.) of policyholders, it is assumed that the claim numbers $N(t)$ are modeled ...
- 115
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1
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409
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How comprehensively do actuarial exams cover quantitative finance?
Some context: The actuarial curriculum offers two papers on quantitative finance (QF):
CT8: Financial Engineering (Utility theory, Measures of risk, MVPT, CAPM, Binomial model, stochastic calculus, ...
- 623
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516
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Normal default probability vs forward default probability/conditional default
is the diagram correct in calculating foward PD(conditional default) ? Or should the formula be
Probability of default = probability of survival x forward PD
Which of this is equal to marginal PD(...
- 11
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75
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Risk-neutral pricing the "un"guaranteed benefits of an insurance policy
I'd love to know if the model of Black-Scholes-Merton could be used to anything that replicates the payoff of a call or option, for example:
An insurance contract with participation ( meaning that ...
- 21
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Find a relationship between the present value and future value of an annuity [closed]
The following is a previous examination question in Financial Mathematics:
If $A, r, n, PV$ and $FV$ represents the ordinary annuity (annuity
immediate) amount, rate of interest, number of years, ...
- 101
2
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1
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329
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Projecting a Thiele differential equation with Black Scholes returns
I am trying to solve the equation
$\frac{d}{dt}V(t)=r(t)V(t)+\pi-\mu(x+t)(b_d-V(t))$
numerically using the R function 'ode'. This is a Thiele differential equation for a life insurance reserve with ...
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What are the essential characteristics of asset prices?
I think the question has already been asked about stylized facts of asset returns; this question regards the essential characteristics and normative assumptions used to evaluate asset prices. I.e., ...
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