  Quantum Monte Carlo integration (QMCI) provides a quadratic speed-up over its
classical counterpart, and its applications have been investigated in various
fields, including finance. This paper considers its application to risk
aggregation, one of the most important numerical tasks in financial risk
management. Risk aggregation combines several risk variables and quantifies the
total amount of risk, taking into account the correlation among them. For this
task, there exists a useful tool called copula, with which the joint
distribution can be generated from marginal distributions with a flexible
correlation structure. Classically, the copula-based method utilizes sampling
of risk variables. However, this procedure is not directly applicable to the
quantum setting, where sampled values are not stored as classical data, and
thus no efficient quantum algorithm is known. In this paper, we propose a
quantum algorithm for copula-based risk aggregation that is compatible with
QMCI. In our algorithm, we first estimate each marginal distribution as a
series of orthogonal functions, where the coefficients can be calculated with
QMCI. Then, by plugging the marginal distributions into the copula and
obtaining the joint distribution, we estimate risk measures using QMCI again.
With this algorithm, nearly quadratic quantum speed-up can be obtained for
sufficiently smooth marginal distributions.
