Estimating Continuation Value for Event-Driven Capital Allocation

# How should an event-driven Kelly allocator price capital reserved for stochastic future signals?


# How should an event-driven Kelly allocator price capital reserved for stochastic future signals?












I am building an event-driven capital allocator for three trading strategies. This is a portfolio-optimization and validation question, not a request for investment advice.

Signals arrive asynchronously. Several signals can be available at the same time, positions lock capital until they close, and the arrival times, holding periods, and returns of future signals are uncertain.

For each current signal $i$, I have:

- a posterior predictive return distribution $R_i$;

- a stop-loss risk estimate;

- an estimated holding period;

- model-level and portfolio-level risk limits.

The allocator must make three related decisions:

- How much free capital should be invested now?

- How much capacity should be reserved for signals that may arrive later?

- How should current capital be divided among simultaneous signals, while generally favoring signals with higher posterior expected value?

My intended objective is long-run geometric growth, subject to explicit drawdown, gross-exposure, per-trade, and per-model constraints. A natural formulation appears to be

$$V_t(s_t)=\max_{x_t \in X(s_t)}\inf_{P \in \mathcal{U}_t}\mathbb{E}_P\left[\log\left(\frac{W_{t+1}}{W_t}\right)+V_{t+1}(s_{t+1})\right].$$

Here, the state includes free capital, open positions, time, and remaining holding periods.

The marginal value of one unit of free capacity would then be a shadow price such as

$$\lambda_t(c)=\frac{\partial V_t(s_t)}{\partial c_{\mathrm{free}}}.$$

The current implementation approximates the continuation-value curve by block-bootstrapping historical sequences of future signal arrivals and applying a greedy recourse allocator to each simulated sequence. Current signals are then allocated with a joint expected-log optimizer.

However, this approach appears to overvalue future capacity.

I have only a few hundred event decisions. In a chronological development test using identical signals and initial capital:

- the trained policy finished with only about 40% of the final wealth of an equal-stop-risk baseline;

- its maximum drawdown was worse, 78.7% versus 73.1%;

- it accepted 176 signals versus 128 for the baseline;

- in a five-seed ablation at the same current-exposure level, setting continuation value to zero outperformed the full continuation model in every seed.

The policy search evaluated 3,000 calibration configurations, but the continuation-value weight itself had been structurally fixed at one. Therefore, the search could not select the empirically superior zero-continuation case.

My main question is:

What statistically defensible, low-sample method would you use to estimate and cross-validate the marginal continuation value of free capital, so that the allocator does not systematically over-reserve for hypothetical future signals while still accounting for their stochastic arrival?

I am particularly interested in whether this should be treated as:

- a dynamic stochastic-knapsack or bid-price problem;

- a receding-horizon stochastic program with an approximate terminal value function; or

- a simpler current-only robust Kelly allocator until continuation value demonstrates out-of-sample value.

A useful answer would ideally describe the state variables, the continuation-value estimator, and an appropriate nested chronological validation procedure. I am not looking for a package recommendation or a neural-network solution.

## Answer by Russlan Ramdowar (score 1)

https://quant.stackexchange.com/a/85775

I'd treat this as approximate dynamic programming, not regular static Kelly sizing.

Keep the state small: free capital, open positions, remaining holding periods, model-level exposure, total portfolio exposure, and maybe one coarse time/regime variable. With only a few hundred decisions, a fancy state model will mostly become a very confident noise machine.

For continuation value, I'd use chronological scenario replay and estimate the marginal value directly. At each historical decision state, replay the same future path twice:

$$ \hat{\lambda}_t(c) = \frac{\hat{V}_t(c+\Delta c)-\hat{V}_t(c)}{\Delta c}. $$

One replay starts with free capital $c$, and the other with $c+\Delta c$. Using the same arrival sequence in both runs gives you a paired estimate, so a lot of simulation noise cancels out.

The important bit: replay the actual policy mechanics -- capital lockups, exits, risk constraints, simultaneous signals, and rejected opportunities. Don't let a greedy future allocator behave like an oracle, because that will naturally overprice spare capacity. It knows too much and makes future opportunities look cleaner than they really are.

Given the sample size, I'd shrink the estimate hard toward zero:

$$ \tilde{\lambda}_t = \alpha \hat{\lambda}_t, \qquad 0 \leq \alpha \leq 1. $$

Choose $\alpha$ out of sample, and make sure zero is included. I'd go one step further and use a conservative lower confidence bound:

$$ \lambda_t^{\mathrm{usable}} = \max\left( 0,\, \tilde{\lambda}_t - z\,\widehat{\mathrm{SE}}(\tilde{\lambda}_t) \right). $$

Basically: reserve capital only if the estimated value of waiting is still positive after accounting for uncertainty. Hypothetical future trades need to earn their seat at the table.

Validation should be nested and chronological:

- Use outer walk-forward folds to measure honest policy performance.

- Inside each training fold, use another chronological split to select the continuation weight, shrinkage, horizon, and reservation cap.

- Refit using only information available before the outer test window.

- Roll forward and repeat.

- Keep one final chronological period completely untouched.

And yeah, the continuation-weight grid absolutely needs to include zero, plus something like $0.1$, $0.25$, $0.5$, and $1$. Running 3,000 configurations doesn't help if all 3,000 hard-code the same structural assumption. Your five-seed ablation is already telling you that zero continuation value is a real candidate, not some silly edge case.

I'd compare against:

- current-only fractional or robust Kelly;

- equal-stop-risk;

- a simple fixed reservation cap;

- the continuation model across multiple weights, including zero.

The primary metric should be out-of-sample cumulative log growth. Then use maximum drawdown, constraint violations, turnover, and fold-by-fold consistency as guardrails. With this little data, I'd care more about repeatable improvement across time blocks than one lucky terminal-wealth result.

Conceptually, this is a stochastic-knapsack or bid-price problem. Practically, I'd implement it as a receding-horizon stochastic program with a heavily regularized terminal value.

But production-wise? I'd keep the current-only robust Kelly allocator as the default until continuation value shows consistent out-of-sample improvement in both log growth and drawdown. Future capacity probably has some option value, but with only a few hundred events, the statistically honest prior is "close to zero until proven otherwise."