论文标题
分支扩散的随机目标问题
A Stochastic Target Problem for Branching Diffusions
论文作者
论文摘要
我们考虑分支扩散过程的最佳随机目标问题。此问题包括找到最小的条件，该条件允许对控件允许下面的分支过程在其每个分支的有限端子时间内达到目标集。这个问题是由金融科技的示例引起的，我们在基于区块链的加密货币上寻找期权的超级复制价格。我们首先陈述了随机目标问题的价值函数的动态编程原理。然后，我们证明可以通过所谓的分支属性将值函数简化为具有有限维度参数的新函数。在广泛的条件下，最后一个功能被证明是HJB变化不等式的独特粘度解决方案。
We consider an optimal stochastic target problem for branching diffusion processes. This problem consists in finding the minimal condition for which a control allows the underlying branching process to reach a target set at a finite terminal time for each of its branches. This problem is motivated by an example from fintech where we look for the super-replication price of options on blockchain based cryptocurrencies. We first state a dynamic programming principle for the value function of the stochastic target problem. We then show that the value function can be reduced to a new function with a finite dimensional argument by a so called branching property. Under wide conditions, this last function is shown to be the unique viscosity solution to an HJB variational inequality.
