\begin{algorithmic}
\Require{$\{M, x_0, x_M, r,\lambda_t, D_{\alpha}, \alpha, \nu, \beta, \lambda, \mu\}$ (Table \ref{tab:parameters})} 
\State{1: Compute Time Steps: $\{\Delta t_k\}_{k=1}^M$ and $\Delta t$}
\State{2: Compute State Steps: $\{ \Delta x_k \}_{k=1}^M$ and $\Delta x$ (Eqn. [\ref{eq:latticesize}]) }
\State{3: Initialise Background Lattice: $(x_i,t_n)$}
\State{4: Compute Initial Conditions: $\varphi^i_0$}
\State{\ForAll{$n$}
    \State{5: Set Time and State Steps: $\Delta t_n, \Delta x_n$}
    \State{6: Compute Boltzmann Potentials: $V_t$}
    \State{7: Compute Jump Probabilities: $r$, $F_n$}
    \State{8: Update Sources: $s(x_i,t_n,p_n)$}
    \State{9: Update Boundary Conditions: $\varphi^0_n$, $\varphi^M_n$}
    \State{10: Update Interior Points: $\varphi^i_n$ (Eqn. [\ref{eq:UpdateEquationExpArrival},\ref{eq:onjumplattice},\ref{eq:MemKerRecursive}])} 
    \State{11: Find mid-price: $p_n=\{ x_i : \min \{|\varphi^i_n|\} \}$}
    \EndFor} \\
\State{\Return{$\varphi^i_n$ and $p_n$ on lattice $(x_i,t_n)$}}
\end{algorithmic}

\begin{algorithmic}
\Require{$\{M, x_0, x_M, r,\lambda_t, D_{\alpha}, \alpha, \nu, \beta, \lambda, \mu\}$ (Table \ref{tab:parameters})}
\State{1: Compute Time Steps: $\{\Delta t_k\}_{k=1}^M$ and $\Delta t$}
\State{2: Compute State Steps: $\{ \Delta x_k \}_{k=1}^M$ and $\Delta x$ (Eqn. [\ref{eq:latticesize}]) }
\State{3: Initialise Background Lattice: $(x_i,t_n)$}
\State{4: Compute Initial Conditions: $\varphi^i_0$}
\State{\ForAll{$n$}
\State{5: Set Time and State Steps: $\Delta t_n, \Delta x_n$}
\State{6: Compute Boltzmann Potentials: $V_t$}
\State{7: Compute Jump Probabilities: $r$, $F_n$}
\State{8: Update Sources: $s(x_i,t_n,p_n)$}
\State{9: Update Boundary Conditions: $\varphi^0_n$, $\varphi^M_n$}
\State{10: Update Interior Points: $\varphi^i_n$ (Eqn. [\ref{eq:UpdateEquationExpArrival},\ref{eq:onjumplattice},\ref{eq:MemKerRecursive}])}
\State{11: Find mid-price: $p_n=\{ x_i : \min \{|\varphi^i_n|\} \}$}
\EndFor} \\
\State{\Return{$\varphi^i_n$ and $p_n$ on lattice $(x_i,t_n)$}}
\end{algorithmic}
{
    "title": "anomalous diffusion and price impact in the fluid-limit of an order book",
    "id": "2310.06079",
    "abstract": "we extend a discrete time random walk (dtrw) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. here using random walks with sibuya waiting times to include a time-dependent stochastic forcing function with non-uniformly sampled times between order book events in the setting of fractional diffusion. this models the fluid limit of an order book by modelling the continuous arrival, cancellation and diffusion of orders in the presence of information shocks. we study the impulse response and stylised facts of orders undergoing anomalous diffusion for different forcing functions and model parameters. concretely, we demonstrate the price impact for flash limit-orders and market orders and show how the numerical method generate kinks in the price impact. we use cubic spline interpolation to generate smoothed price impact curves. the work promotes the use of non-uniform sampling in the presence of diffusive dynamics as the preferred simulation method.",
    "categories": "q-fin.cp cs.ce nlin.ao q-fin.tr",
    "doi": "",
    "created": "2023-10-09",
    "updated": "2024-01-16",
    "authors": [
        "derick diana",
        "tim gebbie"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2310.06079"
}
{
    "ToxicityFilter": {
        "text_to_toxicity_attributes": {
            "Anomalous.sty": {
                "toxicity_score": 0.006942749,
                "severe_toxicity_score": 0.0016117096,
                "identity_attack_score": 0.0010498142,
                "insult_score": 0.0062208683,
                "profanity_score": 0.018665737,
                "threat_score": 0.0057865805,
                "sexually_explicit_score": 0.026067909,
                "flirtation_score": 0.31151596
            },
            "Figures/Tikz/tikz_timescales.tex": {
                "toxicity_score": 0.056016337,
                "severe_toxicity_score": 0.008049011,
                "identity_attack_score": 0.0058086636,
                "insult_score": 0.01819439,
                "profanity_score": 0.11354194,
                "threat_score": 0.008285114,
                "sexually_explicit_score": 0.06306043,
                "flirtation_score": 0.21970871
            },
            "Figures/Tikz/tikz_time1.tex": {
                "toxicity_score": 0.056016337,
                "severe_toxicity_score": 0.008049011,
                "identity_attack_score": 0.0058086636,
                "insult_score": 0.01819439,
                "profanity_score": 0.11354194,
                "threat_score": 0.008285114,
                "sexually_explicit_score": 0.06306043,
                "flirtation_score": 0.21970871
            },
            "Anomalous.bib": {
                "toxicity_score": 0.0076652975,
                "severe_toxicity_score": 0.00069618225,
                "identity_attack_score": 0.002192123,
                "insult_score": 0.006838372,
                "profanity_score": 0.011902207,
                "threat_score": 0.0065050707,
                "sexually_explicit_score": 0.007726009,
                "flirtation_score": 0.27574712
            },
            "Figures/Tikz/tikz_priceimpactkink.tex": {
                "toxicity_score": 0.0131943645,
                "severe_toxicity_score": 0.0013828278,
                "identity_attack_score": 0.0034408006,
                "insult_score": 0.007797878,
                "profanity_score": 0.01627459,
                "threat_score": 0.0076766624,
                "sexually_explicit_score": 0.0129749775,
                "flirtation_score": 0.21643804
            },
            "Figures/Tikz/tikz_time2.tex": {
                "toxicity_score": 0.056016337,
                "severe_toxicity_score": 0.008049011,
                "identity_attack_score": 0.0058086636,
                "insult_score": 0.01819439,
                "profanity_score": 0.11354194,
                "threat_score": 0.008285114,
                "sexually_explicit_score": 0.06306043,
                "flirtation_score": 0.21970871
            },
            "Anomalous.tex": {
                "toxicity_score": 0.04240986,
                "severe_toxicity_score": 0.0029945374,
                "identity_attack_score": 0.01274247,
                "insult_score": 0.014504919,
                "profanity_score": 0.028503597,
                "threat_score": 0.012751401,
                "sexually_explicit_score": 0.034442667,
                "flirtation_score": 0.33611152
            },
            "Figures/Tikz/tikz_nonuniform.tex": {
                "toxicity_score": 0.014011159,
                "severe_toxicity_score": 0.0013160706,
                "identity_attack_score": 0.0032373124,
                "insult_score": 0.0075888764,
                "profanity_score": 0.015523086,
                "threat_score": 0.0074436385,
                "sexually_explicit_score": 0.013151909,
                "flirtation_score": 0.3190365
            },
            "Figures/Tikz/tikz_time3-1.tex": {
                "toxicity_score": 0.056016337,
                "severe_toxicity_score": 0.008049011,
                "identity_attack_score": 0.0058086636,
                "insult_score": 0.01819439,
                "profanity_score": 0.11354194,
                "threat_score": 0.008285114,
                "sexually_explicit_score": 0.06306043,
                "flirtation_score": 0.21970871
            },
            "Anomalous.bbl": {
                "toxicity_score": 0.012566062,
                "severe_toxicity_score": 0.0011634827,
                "identity_attack_score": 0.004162259,
                "insult_score": 0.007607877,
                "profanity_score": 0.014874061,
                "threat_score": 0.007637825,
                "sexually_explicit_score": 0.011736456,
                "flirtation_score": 0.21238147
            },
            "Figures/Tikz/tikz_time3-2.tex": {
                "toxicity_score": 0.056016337,
                "severe_toxicity_score": 0.008049011,
                "identity_attack_score": 0.0058086636,
                "insult_score": 0.01819439,
                "profanity_score": 0.11354194,
                "threat_score": 0.008285114,
                "sexually_explicit_score": 0.06306043,
                "flirtation_score": 0.21970871
            }
        },
        "reason": null
    }
}
{
    "num_done": {
        "figure": 0,
        "algorithm": 2,
        "plot": 3
    }
}
{
    "NonTrivialRenderingFilter": {
        "white_pixels_ratio": 88.97126164007193,
        "hash": "f9dff9f1c1010f39",
        "most_frequent_color_ratio": 88.97126164007193
    }
}