arXiv subjects

Tak Kuen Siu

Publications and source records attributed to Tak Kuen Siu.

4 recordsLinked to original sources

arXiv2026

Arbitrage-free catastrophe reinsurance valuation for compound dynamic contagion claims

In this paper, we consider catastrophe stop-loss reinsurance valuation for a reinsurance company with dynamic contagion claims. To deal with conventional and emerging catastrophic events, we propose the use of a compound dynamic contagion process for the catastrophic component of the liability. Under the premise that there is an absence of arbitrage opportunity in the market, we obtain arbitrage-free premiums for these contracts. To this end, the Esscher transform is adopted to specify an equivalent martingale probability measure. We show that reinsurers have various ways of levying the security loading on the net premiums to quantify the catastrophic liability in light of the growing challenges posed by emerging risks arising from climate change, cyberattacks, and pandemics. We numerically compare arbitrage-free catastrophe stop-loss reinsurance premiums via the Monte Carlo simulation method. We also compare them with those from generalised compound Hawkes/compound Cox cases. Sensitivity analyses are performed by changing the retention level, the Esscher parameters and the intensity parameters.

q-fin.RM↗

arXiv2025

Optimal Investment, Consumption, and Insurance with Durable Goods under Stochastic Depreciation Risk

We study an infinite-horizon optimal investment, consumption and insurance problem for an economic agent who consumes a perishable and a durable good. The agent trades in a risk-free asset, a risky asset, and a durable good whose price follows a correlated diffusion, while the stock of the durable good depreciates deterministically and is subject to insurable Poisson loss shocks. The agent can partially hedge these shocks via an insurance contract with loading and chooses optimal perishable consumption, portfolio holdings, and insurance coverage to maximise expected discounted CRRA utility. Exploiting the homogeneity of the problem, we reduce the Hamilton--Jacobi--Bellman equation to a static one-dimensional optimisation over constant portfolio shares and derive a semi-explicit optimal strategy. We then prove a verification theorem for the associated jump-diffusion wealth process with insurance, establishing the existence and optimality of this constant-fraction strategy under explicit transversality conditions for both risk-aversion regimes $0<γ<1$ and $γ>1$. Numerical experiments illustrate the impact of stochastic depreciation risk and insurance loading on the optimal allocation to financial assets, durable goods, and insurance coverage.

econ.GN↗

arXiv2023

A nonlinearity and model specification test for functional time series

An important issue in functional time series analysis is whether an observed series comes from a purely random process. We extend the BDS test, a widely-used nonlinear independence test, to the functional time series. Like the BDS test in the univariate case, the functional BDS test can act as the model specification test to evaluate the adequacy of various prediction models and as a nonlinearity test to detect the existence of nonlinear structures in a functional time series after removing the linear structure exhibited. We show that the test statistic from the functional BDS test has the same asymptotic properties as those in the univariate case and provides the recommended range of its hyperparameters. Additionally, empirical data analysis features its applications in evaluating the adequacy of the fAR(1) and fGARCH(1,1) models in fitting the daily curves of cumulative intraday returns (CIDR) of the VIX index. We showed that the functional BDS test remedies the weakness of the existing independence test in the literature, as the latter is restricted in detecting linear structures, thus, can neglect nonlinear temporal structures.

stat.ME↗

arXiv2021

Regime Switching Optimal Growth Model with Risk Sensitive Preferences

We consider a risk-sensitive optimization of consumption-utility on infinite time horizon where the one-period investment gain depends on an underlying economic state whose evolution over time is assumed to be described by a discrete-time, finite-state, Markov chain. We suppose that the production function also depends on a sequence of i.i.d. random shocks. For the sake of generality, the utility and the production functions are allowed to be unbounded from above. Under the Markov regime-switching model, it is shown that the value function of optimization problem satisfies an optimality equation and that the optimality equation has a unique solution in a particular class of functions. Furthermore, we show that an optimal policy exists in the class of stationary policies. We also derive the Euler equation of optimal consumption. Furthermore, the existence of the unique joint stationary distribution of the optimal growth process and the underlying regime process is examined. Finally, we present a numerical solution by considering power utility and some hypothetical values of parameters in a regime switching extension of Cobb-Douglas production rate function.

math.OC↗