How should static Kelly sizing be extended to asynchronous trading signals with capital lock-up and stochastic future arrivals?

I am designing an event-driven capital allocator for several trading strategies. I currently have three strategies, although the allocator should eventually support additional ones. This is a mathematical modeling question, not a request for investment advice, a package recommendation, or help debugging an existing implementation. Available information Each strategy generates signals at a different and uncertain frequency. For each signal $i$ , I can estimate: a predictive distribution for its net return per dollar of notional, $R_i$ , including transaction costs; a stop-loss loss fraction, $s_i$ ; a distribution or estimate of its holding time, $H_i$ ; the strategy that generated it; the historical arrival process of signals from that strategy. I use expected log return as the geometric-growth measure: $$ \ell_i

\mathbb{E}\left[\log(1+R_i)\right]. $The corresponding geometric mean return is$ \exp(\ell_i)-1. $A possible descriptive score for comparing signals with different holding periods is$ \rho_i

\frac{ \mathbb{E}\left[\log(1+R_i)\right] }{ \mathbb{E}[H_i] }. However, I do not assume that ranking or sizing trades by $\rho_i$ is optimal. Such a ratio may be meaningful for isolated sequential opportunities, but my positions can overlap and compete for the same capital. I also understand that a scalar expected log return is not sufficient for position sizing. The dispersion, downside tail, dependence between simultaneous trades, and estimation uncertainty of the return distributions should matter. Event-driven setting Signals arrive asynchronously. Several signals can arrive at the same time, while positions opened earlier may still be active. Capital allocated to a position remains unavailable until that position closes. Consequently, accepting a positive-expected-growth signal now has an opportunity cost: it may prevent the allocator from accepting a better signal that arrives before the first position closes. At an event time $t$ , let: $W_t$ be total portfolio wealth; $C_t$ be capital currently available for new positions; $\mathcal{P}_t$ be the set of open positions; $\mathcal{A}_t$ be the set of newly available signals; $x_{i,t}$ be the notional allocated to signal $i \in \mathcal{A}_t$ . The allocation vector $x_t$ simultaneously determines the three decisions I care about. First, the amount invested now is I_t

\sum_{i \in \mathcal{A}t} x{i,t}. $Second, the amount kept available for future signals is$ C_t-I_t. Third, the individual values $x_{i,t}$ determine how current exposure is distributed across simultaneous signals. At a minimum, the allocations must satisfy x_{i,t} \geq 0, \qquad \sum_{i \in \mathcal{A}t} x{i,t} \leq C_t. If $D_t$ denotes the existing stop-loss risk from open positions and $B_t$ is the permitted portfolio stop-risk budget, another constraint could be D_t + \sum_{i \in \mathcal{A}t} s_i x{i,t} \leq B_t. $Additional limits may apply to gross exposure, individual trades, and individual strategies. When a position closes, its capital is released and its realized profit or loss changes portfolio wealth. New decisions are then made using only the information available at that time. Objective The economic objective is to maximize long-run geometric growth per unit of calendar time. A possible formal objective is$ \sup_{\pi} \liminf_{T \to \infty} \frac{1}{T} \mathbb{E}_{\pi} \left[ \log\left(\frac{W_T}{W_0}\right) \right], where $\pi$ is an allocation policy mapping the observable portfolio state and current signals to their notionals. For a static one-period problem, let $b$ denote the fractions of wealth allocated to a vector of opportunities with joint return vector $R$ . If all opportunities are known and resolve over the same period, I understand the standard log-optimal formulation to be \max_b \mathbb{E} \left[ \log\left(1+b^\top R\right) \right],

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