We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and Hull-White interest rate. We verify the validity of the actuarial approach to the European vanilla option for non-tradable assets. The formulas of the actuarial approach to the reload option are derived from the fair premium principle and the obtained results are arbitrage. Numerical experiments are conducted to analyze the effects of different parameters on the results of valuation as well as their differences from those obtained by the no-arbitrage approach. Finally, we give the valuations of the reload options under different parameters.
Let G be a graph and k ≥ 2 a positive integer. Let h:E(G) →[0, 1] be a function. If holds for each x ∈ V (G), then we call G[F_{h}] a fractional k-factor of G with indicator function h where F_{h}={e ∈ E(G):h(e) > 0}. A graph G is fractional independent-set-deletable k-factor-critical (in short, fractional ID-k-factor-critical), if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n ≥ 9k-14 and for any subset X⊂V(G) we have
then G is fractional ID-k-factor-critical.